context stringlengths 250 4.63k | A stringlengths 250 6.41k | B stringlengths 250 5.14k | C stringlengths 250 3.8k | D stringlengths 250 8.2k | label stringclasses 4
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that adds the results of 1+(n−m)/21𝑛𝑚21+(n-m)/21 + ( italic_n - italic_m ) / 2
Gaussian integrations for moments xD−1+n−2ssuperscript𝑥𝐷1𝑛2𝑠x^{D-1+n-2s}italic_x start_POSTSUPERSCRIPT italic_D - 1 + italic_n - 2 italic_s end_POSTSUPERSCRIPT. The disadvantage | {n,n^{\prime}}.∫ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT italic_x start_POSTSUPERSCRIPT italic_D - 1 end_POSTSUPERSCRIPT italic_R start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT ( italic_x ) italic_R start_POSTSUBSCRIPT italic... |
Gaussian integration rules for integrals ∫01xD−1Rnm(x)f(x)𝑑xsuperscriptsubscript01superscript𝑥𝐷1superscriptsubscript𝑅𝑛𝑚𝑥𝑓𝑥differential-d𝑥\int_{0}^{1}x^{D-1}R_{n}^{m}(x)f(x)dx∫ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT italic_x start_POSTSUPERSCRIPT italic_D - 1 ... | +x\left[D-1-(D+1)x^{2}\right]\frac{d}{dx}R_{n}^{m}(x).start_ROW start_CELL italic_x start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( italic_x start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT - 1 ) divide start_ARG italic_d start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG start_ARG italic_d italic_x start_POSTSUPERSCRIPT 2 e... | rules for
the lifted integrals ∫01xD−1[1+Rnm(x)]f(x)𝑑xsuperscriptsubscript01superscript𝑥𝐷1delimited-[]1superscriptsubscript𝑅𝑛𝑚𝑥𝑓𝑥differential-d𝑥\int_{0}^{1}x^{D-1}[1+R_{n}^{m}(x)]f(x)dx∫ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT italic_x start_POSTSUPERSCRIPT ita... | D |
On the other hand, if the instruction Itsubscript𝐼𝑡I_{t}italic_I start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT was Show(A)Show𝐴\operatorname{Show}(A)roman_Show ( italic_A ) then Eval(S,M,s,t)Eval𝑆𝑀𝑠𝑡\operatorname{Eval}(S,M,s,t)roman_Eval ( italic_S , italic_M , italic_s , italic_t ) is
defined to be the list ... | This adds only one extra MSLP instruction, in order to form and store the element xv−1𝑥superscript𝑣1xv^{-1}italic_x italic_v start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT needed in the conjugate on the right-hand side of (2) (this element can later be overwritten and so does not add to the overall maximum memory quo... | does not yield an upper bound for the memory requirement in a theoretical analysis.
Moreover, the result of SlotUsagePattern improves the memory usage but it is not necessarily optimized overall and, hence, the number of slots can still be greater than the number of slots of a carefully computed MSLP. It should also be... |
Instruction type (i) above simply copies an element already in memory to a different memory slot. These instructions can arguably be disregarded for the purpose of determining the length of an MSLP, because in a practical implementation they could be handled via relabelling. |
For the purposes of determining the cost of Taylor’s algorithm in terms of matrix operations, namely determining the length of an MSLP for the algorithm, we assume that the field elements −gicgrc−1subscript𝑔𝑖𝑐superscriptsubscript𝑔𝑟𝑐1-g_{ic}g_{rc}^{-1}- italic_g start_POSTSUBSCRIPT italic_i italic_c end_POSTSU... | C |
where Ω⊂ℝdΩsuperscriptℝ𝑑\Omega\subset\mathbb{R}^{d}roman_Ω ⊂ blackboard_R start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT with d=2𝑑2d=2italic_d = 2 or 3333 for simplicity, and is an open bounded domain with polyhedral boundary ∂ΩΩ\partial\Omega∂ roman_Ω, the symmetric tensor 𝒜∈[L∞(Ω)]symd×d𝒜superscriptsubscrip... | In [MR2718268] is shown that the number of eigenvalues that are very large is related to the number of connected sub-regions on τ¯∪τ¯′¯𝜏superscript¯𝜏′\bar{\tau}\cup{\bar{\tau}}^{\prime}over¯ start_ARG italic_τ end_ARG ∪ over¯ start_ARG italic_τ end_ARG start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT with large coefficien... |
As in many multiscale methods previously considered, our starting point is the decomposition of the solution space into fine and coarse spaces that are adapted to the problem of interest. The exact definition of some basis functions requires solving global problems, but, based on decaying properties, only local comput... | One difficulty that hinders the development of efficient methods is the presence of high-contrast coefficients [MR3800035, MR2684351, MR2753343, MR3704855, MR3225627, MR2861254]. When LOD or VMS methods are considered, high-contrast coefficients might slow down the exponential decay of the solutions, making the method ... | It is hard to approximate such problem in its full generality using numerical methods, in particular because of the low regularity of the solution and its multiscale behavior. Most convergent proofs either assume extra regularity or special properties of the coefficients [AHPV, MR3050916, MR2306414, MR1286212, babuos85... | D |
On the contrary, we may need to use a function θ𝜃\thetaitalic_θ of variable (b,c)𝑏𝑐(b,c)( italic_b , italic_c ); see the description of 𝖪𝗂𝗅𝗅Fsubscript𝖪𝗂𝗅𝗅𝐹\mathsf{Kill}_{F}sansserif_Kill start_POSTSUBSCRIPT italic_F end_POSTSUBSCRIPT in subsection 3.1 for an example.
As such, the flow of Rotate-and-Kill is ... |
Alg-A has simpler primitives because (1) the candidate triangles considered in it have all corners lying on P𝑃Pitalic_P’s vertices and (2) searching the next candidate from a given one is much easier – the code length for this is 1:7 in Alg-A and in Alg-CM. | Comparing the description of the main part of Alg-A (the 7 lines in Algorithm 1) with that of Alg-CM (pages 9–10 of [8]),
Alg-A is conceptually simpler. Alg-CM is claimed “involved” by its authors as it contains complicated subroutines for handling many subcases. | We think Alg-A is better in almost every aspect. This is because it is essentially simpler.
Among other merits, Alg-A is much faster, because it has a smaller constant behind the asymptotic complexity O(n)𝑂𝑛O(n)italic_O ( italic_n ) than the others: |
Our experiment shows that the running time of Alg-A is roughly one eighth of the running time of Alg-K, or one tenth of the running time of Alg-CM. (Moreover, the number of iterations required by Alg-CM and Alg-K is roughly 4.67 times that of Alg-A.) | C |
We observe that at certain points in time, the volume of rumor-related tweets (for sub-events) in the event stream surges. This can lead to false positives for techniques that model events as the aggregation of all tweet contents; that is undesired at critical moments. We trade-off this by debunking at single tweet le... |
As observed in [19, 20], rumor features are very prone to change during an event’s development. In order to capture these temporal variabilities, we build upon the Dynamic Series-Time Structure (DSTS) model (time series for short) for feature vector representation proposed in [20]. We base our credibility feature on t... |
Most relevant for our work is the work presented in [20], where a time series model to capture the time-based variation of social-content features is used. We build upon the idea of their Series-Time Structure, when building our approach for early rumor detection with our extended dataset, and we provide a deep analys... |
In this work, we propose an effective cascaded rumor detection approach using deep neural networks at tweet level in the first stage and wisdom of the “machines”, together with a variety of other features in the second stage, in order to enhance rumor detection performance in the early phase of an event. The proposed ... | at an early stage. Our fully automatic, cascading rumor detection method follows
the idea on focusing on early rumor signals on text contents; which is the most reliable source before the rumors widely spread. Specifically, we learn a more complex representation of single tweets using Convolutional Neural Networks, tha... | C |
The convergence of the direction of gradient descent updates to the maximum L2subscript𝐿2L_{2}italic_L start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT margin solution, however is very slow compared to the convergence of training loss, which explains why it is worthwhile
continuing to optimize long after we have zero training ... | decreasing loss, as well as for multi-class classification with cross-entropy loss. Notably, even though the logistic loss and the exp-loss behave very different on non-separable problems, they exhibit the same behaviour for separable problems. This implies that the non-tail
part does not affect the bias. The bias is a... | Let ℓℓ\ellroman_ℓ be the logistic loss, and 𝒱𝒱\mathcal{V}caligraphic_V be an independent validation set, for which ∃𝐱∈𝒱𝐱𝒱\exists\mathbf{x}\in\mathcal{V}∃ bold_x ∈ caligraphic_V such that 𝐱⊤𝐰^<0superscript𝐱top^𝐰0\mathbf{x}^{\top}\hat{\mathbf{w}}<0bold_x start_POSTSUPERSCRIPT ⊤ end_POSTSUPERSCRIPT over^ start_... | The follow-up paper (Gunasekar et al., 2018) studied this same problem with exponential loss instead of squared loss. Under additional assumptions on the asymptotic convergence of update directions and gradient directions, they were able to relate the direction of gradient descent iterates on the factorized parameteriz... | We should not rely on plateauing of the training loss or on the loss (logistic or exp or cross-entropy) evaluated on a validation data, as measures to decide when to stop. Instead, we should look at the 00–1111 error on the validation dataset. We might improve the validation and test errors even when when the decrease ... | D |
To overcome this issue, we set up a threshold 72 hours. We only consider the first candidate within 72 hours before or after the beginning time of the event as timestamp of human confirming rumors. On average the human editors of Snopes need 25.49 hours to verify the rumors and post it. Our system already achieves 87% ... |
We observe that at certain points in time, the volume of rumor-related tweets (for sub-events) in the event stream surges. This can lead to false positives for techniques that model events as the aggregation of all tweet contents; that is undesired at critical moments. We trade-off this by debunking at single tweet le... | the idea on focusing on early rumor signals on text contents; which is the most reliable source before the rumors widely spread. Specifically, we learn a more complex representation of single tweets using Convolutional Neural Networks, that could capture more hidden meaningful signal than only enquiries to debunk rumor... |
At 18:22 CEST, the first tweet was posted. There might be some certain delay, as we retrieve only tweets in English and the very first tweets were probably in German. The tweet is ”Sadly, i think there’s something terrible happening in #Munich #Munchen. Another Active Shooter in a mall. #SMH”. | The time period of a rumor event is sometimes fuzzy and hard to define. One reason is a rumor may have been triggered for a long time and kept existing, but it did not attract public attention. However it can be triggered by other events after a uncertain time and suddenly spreads as a bursty event. E.g., a rumor999htt... | C |
\mathcal{C}_{k}|a,t)\sum\limits_{l=1}^{m}P(\mathcal{T}_{l}|a,t,\mathcal{C}_{k}%
)\hat{y_{a}},y_{a})sansserif_f start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT = roman_arg roman_min start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT ∑ start_POSTSUBSCRIPT ∀ italic_a end_POSTSUBSCRIPT caligraphic_L ( ∑ start_POSTSUBSCRIPT italic_... | Learning a single model for ranking event entity aspects is not effective due to the dynamic nature of a real-world event driven by a great variety of multiple factors. We address two major factors that are assumed to have the most influence on the dynamics of events at aspect-level, i.e., time and event type. Thus, we... | We further investigate the identification of event time, that is learned on top of the event-type classification. For the gold labels, we gather from the studied times with regards to the event times that is previously mentioned. We compare the result of the cascaded model with non-cascaded logistic regression. The res... | For this part, we first focus on evaluating the performance of single L2R models that are learned from the pre-selected time (before, during and after) and types (Breaking and Anticipate) set of entity-bearing queries. This allows us to evaluate the feature performance i.e., salience and timeliness, with time and type ... | Multi-Criteria Learning. Our task is to minimize the global relevance loss function, which evaluates the overall training error, instead of assuming the independent loss function, that does not consider the correlation and overlap between models. We adapted the L2R RankSVM [12]. The goal of RankSVM is learning a linear... | D |
In this case, the agent must sequentially learn both the underlying dynamics (La,Σa;∀asubscript𝐿𝑎subscriptΣ𝑎for-all𝑎L_{a},\Sigma_{a};\forall aitalic_L start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT , roman_Σ start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT ; ∀ italic_a)
and the conditional reward function’s variance ... | We observe noticeable (almost linear) regret increases when the dynamics of the parameters swap the identity of the optimal arm.
However, SMC-based Thompson sampling and Bayes-UCB agents are able to learn the evolution of the dynamic latent parameters, | We now describe in detail how to use the SMC-based posterior random measure pM(θt+1,a|ℋ1:t)subscript𝑝𝑀conditionalsubscript𝜃𝑡1𝑎subscriptℋ:1𝑡p_{M}(\theta_{t+1,a}|\mathcal{H}_{1:t})italic_p start_POSTSUBSCRIPT italic_M end_POSTSUBSCRIPT ( italic_θ start_POSTSUBSCRIPT italic_t + 1 , italic_a end_POSTSUBSCRIPT | cali... | For the more interesting case of unknown parameters,
we marginalize parameters Lasubscript𝐿𝑎L_{a}italic_L start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT and ΣasubscriptΣ𝑎\Sigma_{a}roman_Σ start_POSTSUBSCRIPT italic_a end_POSTSUBSCRIPT of the transition distributions | If the support of q(⋅)𝑞⋅q(\cdot)italic_q ( ⋅ ) includes the support of the distribution of interest p(⋅)𝑝⋅p(\cdot)italic_p ( ⋅ ), one computes the IS estimator of a test function based on the normalized weights w(m)superscript𝑤𝑚w^{(m)}italic_w start_POSTSUPERSCRIPT ( italic_m ) end_POSTSUPERSCRIPT,
| A |
Table 2 gives an overview of the number of different measurements that are available for each patient.111For patient 9, no data is available.
The study duration varies among the patients, ranging from 18 days, for patient 8, to 33 days, for patient 14. | These are also the patients who log glucose most often, 5 to 7 times per day on average compared to 2-4 times for the other patients.
For patients with 3-4 measurements per day (patients 8, 10, 11, 14, and 17) at least a part of the glucose measuremtents after the meals is within this range, while patient 12 has only t... | Median number of blood glucose measurements per day varies between 2 and 7. Similarly, insulin is used on average between 3 and 6 times per day.
In terms of physical activity, we measure the 10 minute intervals with at least 10 steps tracked by the google fit app. | Patient 17 has more rapid insulin applications than glucose measurements in the morning and particularly in the late evening.
For patient 15, rapid insulin again slightly exceeds the number of glucose measurements in the morning. Curiously, the number of glucose measurements match the number carbohydrate entries – it i... | Likewise, the daily number of measurements taken for carbohydrate intake, blood glucose level and insulin units vary across the patients.
The median number of carbohydrate log entries vary between 2 per day for patient 10 and 5 per day for patient 14. | D |
Our proposed encoder-decoder model clearly demonstrated competitive performance on two datasets towards visual saliency prediction. The ASPP module incorporated multi-scale information and global context based on semantic feature representations, which significantly improved the results both qualitatively and quantita... | To assess the predictive performance for eye tracking measurements, the MIT saliency benchmark Bylinskii et al. (2015) is commonly used to compare model results on two test datasets with respect to prior work. Final scores can then be submitted on a public leaderboard to allow fair model ranking on eight evaluation met... | Later attempts addressed that shortcoming by taking advantage of classification architectures pre-trained on the ImageNet database Deng et al. (2009). This choice was motivated by the finding that features extracted from CNNs generalize well to other visual tasks Donahue et al. (2014). Consequently, DeepGaze I Kümmerer... | Further improvements of benchmark results could potentially be achieved by a number of additions to the processing pipeline. Our model demonstrates a learned preference for predicting fixations in central regions of images, but we expect performance gains from modeling the central bias in scene viewing explicitly Kümme... | For related visual tasks such as semantic segmentation, information distributed over convolutional layers at different levels of the hierarchy can aid the preservation of fine spatial details Hariharan et al. (2015); Long et al. (2015). The prediction of fixation density maps does not require accurate class boundaries ... | C |
Finally, we have to show that in this pd-marking scheme, the maximum number of activeactive\operatorname{\texttt{active}}act positions is bounded by 2k+12𝑘12k+12 italic_k + 1. This is obviously true at step p1subscript𝑝1p_{1}italic_p start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT. Now let s𝑠sitalic_s with 1≤s≤|α|−11𝑠𝛼11... | j𝑗jitalic_j joins two blocks of size 1111: the number of activeactive\operatorname{\texttt{active}}act positions increases by 1111.
This is due to the fact that by setting j𝑗jitalic_j to activeactive\operatorname{\texttt{active}}act, we do not create any internal activeactive\operatorname{\texttt{active}}act position... | We first prove pw(Gα)≤2loc(α)pwsubscript𝐺𝛼2loc𝛼\operatorname{\textsf{pw}}(G_{\alpha})\leq 2\operatorname{\textsf{loc}}(\alpha)pathwidth ( italic_G start_POSTSUBSCRIPT italic_α end_POSTSUBSCRIPT ) ≤ 2 loc ( italic_α ). Intuitively speaking, we will translate the stages of a marking sequence σ𝜎\sigmaitalic_σ for α... | This completes the definition of the marking scheme. Figure 7 contains an example of how step ps+1subscript𝑝𝑠1p_{s+1}italic_p start_POSTSUBSCRIPT italic_s + 1 end_POSTSUBSCRIPT is obtained from step pssubscript𝑝𝑠p_{s}italic_p start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT. In this example, we first set extending po... |
In the first phase of the marking scheme, i. e., the phase where we only set extending positions to activeactive\operatorname{\texttt{active}}act, the following different situations can arise, whenever we set some position j𝑗jitalic_j to activeactive\operatorname{\texttt{active}}act (see Figure 7 for an illustration)... | D |
Zubair et al.[75] detected the R-peak using a non-linear transformation and formed a beat segment around it.
Then, they used the segments to train a three layer 1D CNN with variable learning rate depending on the mean square error and achieved better results than previous state-of-the-art. | In their article Kiranyaz et al.[77] trained patient-specific CNNs that can be used to classify long ECG data stream or for real-time ECG monitoring and early alert system on a wearable device.
The CNN consisted of three layers of an adaptive implementation of 1D convolution layers. | Taji et al.[91] trained a DBN to classify acceptable from unacceptable ECG segments to reduce the false alarm rate caused by poor quality ECG during AF detection.
Eight different levels of ECG quality are provided by contaminating ECG with motion artifact from the NSTDB for validation. | Another three models were trained using the signals as 1D.
The first model was a FNN with dropout, the second a three layer 1D CNN and the third a 2D CNN same as the first but trained with a stacked version of the signal (also trained with data augmentation). | Experiments by the authors showed that the three layer 1D CNN created better and more stable results.
In[101] the authors trained a network with an one convolutional layer with dropout followed by two RNNs to identify stress using short-term ECG data. | A |
Our predictive model has stochastic latent variables so it can be applied in highly stochastic environments. Studying such environments is an exciting direction for future work, as is the study of other ways in which the predictive neural network model could be used. Our approach uses the model as a learned simulator a... | The results in these figures are generated by averaging 5555 runs for each game.
The model-based agent is better than a random policy for all the games except Bank Heist. Interestingly, we observed that the best of the 5555 runs was often significantly better. For 6666 of the games, it exceeds the average human score (... | In our empirical evaluation, we find that SimPLe is significantly more sample-efficient than a highly tuned version of the state-of-the-art Rainbow algorithm (Hessel et al., 2018) on almost all games. In particular, in low data regime of 100100100100k samples, on more than half of the games, our method achieves a score... |
The primary evaluation in our experiments studies the sample efficiency of SimPLe, in comparison with state-of-the-art model-free deep RL methods in the literature. To that end, we compare with Rainbow (Hessel et al., 2018; Castro et al., 2018), which represents the state-of-the-art Q-learning method for Atari games, ... |
While SimPLe is able to learn more quickly than model-free methods, it does have limitations. First, the final scores are on the whole lower than the best state-of-the-art model-free methods. This can be improved with better dynamics models and, while generally common with model-based RL algorithms, suggests an import... | D |
However more work needs to be done for full replacing non-trainable S2Is, not only from the scope of achieving higher accuracy results but also increasing the interpretability of the model.
Another point of reference is that the combined models were trained from scratch based on the hypothesis that pretrained low level... | For the purposes of this paper and for easier future reference we define the term Signal2Image module (S2I) as any module placed after the raw signal input and before a ‘base model’ which is usually an established architecture for imaging problems.
An important property of a S2I is whether it consists of trainable para... | Future work could include testing this hypothesis by initializing a ‘base model’ using transfer learning or other initialization methods.
Moreover, trainable S2Is and 1D ‘base model’ variations could also be used for other physiological signals besides EEG such as Electrocardiography, Electromyography and Galvanic Skin... | This is achieved with the use of multilayer networks, that consist of million parameters [1], trained with backpropagation [2] on large amount of data.
Although deep learning is mainly used in biomedical images there is also a wide range of physiological signals, such as Electroencephalography (EEG), that are used for ... | However more work needs to be done for full replacing non-trainable S2Is, not only from the scope of achieving higher accuracy results but also increasing the interpretability of the model.
Another point of reference is that the combined models were trained from scratch based on the hypothesis that pretrained low level... | B |
Hybrid robots typically transition between locomotion modes either by “supervised autonomy” [11], where human operators make the switch decisions, or the autonomous locomotion mode transition approach, where robots autonomously swap the modes predicated on pre-set criteria [8]. However, the execution of supervised con... | There are two primary technical challenges in the wheel/track-legged robotics area [2]. First, there’s a need to ensure accurate motion control within both rolling and walking locomotion modes [5] and effectively handle the transitions between them [6]. Second, it’s essential to develop decision-making frameworks that ... | The Cricket robot, as referenced in [20], forms the basis of this study, being a fully autonomous track-legged quadruped robot. Its design specificity lies in embodying fully autonomous behaviors, and its locomotion system showcases a unique combination of four rotational joints in each leg, which can be seen in Fig. 3... |
Hybrid robots typically transition between locomotion modes either by “supervised autonomy” [11], where human operators make the switch decisions, or the autonomous locomotion mode transition approach, where robots autonomously swap the modes predicated on pre-set criteria [8]. However, the execution of supervised con... | A major obstacle in achieving seamless autonomous locomotion transition lies in the need for an efficient sensing methodology that can promptly and reliably evaluate the interaction between the robot and the terrain, referred to as terramechanics. These methods generally involve performing comprehensive on-site measure... | D |
For paid exchanges at the beginning of the phase, Tog incurs a cost that is less than m2superscript𝑚2m^{2}italic_m start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT. Before serving the last request σℓsubscript𝜎ℓ\sigma_{\ell}italic_σ start_POSTSUBSCRIPT roman_ℓ end_POSTSUBSCRIPT of the phase, the access cost of Tog is less ... |
In an ignoring phase, the cost of Tog for the phase is in the range (βm3,βm3(1+1/m2))𝛽superscript𝑚3𝛽superscript𝑚311superscript𝑚2(\beta m^{3},\beta m^{3}(1+1/m^{2}))( italic_β italic_m start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT , italic_β italic_m start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT ( 1 + 1 / italic_m ... |
The worst-case ratio between the costs of Tog and Mtf2 is maximized when the last phase is an ignoring phase. In this case, we have k𝑘kitalic_k trusting phases and k𝑘kitalic_k ignoring phases. The total cost of Mtf2 is at least km3+k(βm3/2−m2)=km3(1+β/2−1/m)𝑘superscript𝑚3𝑘𝛽superscript𝑚32superscript𝑚2𝑘sup... |
For a trusting phase, the cost of Tog is in the range (m3,m3(1+1/m+1/m2))superscript𝑚3superscript𝑚311𝑚1superscript𝑚2(m^{3},m^{3}(1+1/m+1/m^{2}))( italic_m start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT , italic_m start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT ( 1 + 1 / italic_m + 1 / italic_m start_POSTSUPERSCRIPT 2 en... | Similar arguments apply for an ignoring phase with the exception that the threshold is β⋅m2⋅𝛽superscript𝑚2\beta\cdot m^{2}italic_β ⋅ italic_m start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT and there are no paid exchanges performed by Tog. So, we can observe the following.
| D |
Regarding the support that SS3 provides for early classification we can say that, even though the rules we used are very simple, they are more effective than more elaborated and complex mechanisms used in the pilot task. For instance, some mechanisms to stop reading and classifying a subject included complex decision m... | Regarding document representations some research groups used simple features like standard Bag of Words [Trotzek et al., 2017, Villegas et al., 2017, Farıas-Anzaldúa et al., 2017], bigrams and trigrams [Villegas et al., 2017, Almeida et al., 2017, Farıas-Anzaldúa et al., 2017], while others used more elaborated and dom... | Most research groups [Malam et al., 2017, Trotzek et al., 2017, Sadeque et al., 2017, Villatoro-Tello et al., 2017, Villegas et al., 2017, Almeida et al., 2017] applied a simple policy in which, the same way as in [Losada & Crestani, 2016], a subject is classified as depressed when the classifier outputs a value greate... | Regarding classification models, some groups used standard classifiers777Such as Multinomial Naive Bayes(MNB), Logistic Regression (LOGREG), Support Vector Machine(SVM), Random Forest, Decision Trees, etc.[Malam et al., 2017, Trotzek et al., 2017, Sadeque et al., 2017, Villegas et al., 2017, Almeida et al., 2017, Farıa... | It is true that more elaborated methods that simultaneously learn the classification model and the policy to stop reading could have been used, such as in [Dulac-Arnold et al., 2011, Yu et al., 2017].
However, for the moment it is clear that this very simple approach is effective enough to outperform the remainder meth... | D |
Stochastic gradient descent (SGD) and its variants (Robbins and Monro, 1951; Bottou, 2010; Johnson and Zhang, 2013; Zhao et al., 2018, 2020, 2021) have been the dominating optimization methods for solving (1).
In each iteration, SGD calculates a (mini-batch) stochastic gradient and uses it to update the model parameter... | Furthermore, when we distribute the training across multiple workers, the local objective functions may differ from each other due to the heterogeneous training data distribution. In Section 5, we will demonstrate that the global momentum method outperforms its local momentum counterparts in distributed deep model trai... | Recently, parameter server (Li et al., 2014) has been one of the most popular distributed frameworks in machine learning. GMC can also be implemented on the parameter server framework.
In this paper, we adopt the parameter server framework for illustration. The theories in this paper can also be adapted for the all-red... | With the rapid growth of data, distributed SGD (DSGD) and its variant distributed MSGD (DMSGD) have garnered much attention. They distribute the stochastic gradient computation across multiple workers to expedite the model training.
These methods can be implemented on distributed frameworks like parameter server and al... | GMC can be easily implemented on the all-reduce distributed framework in which each worker sends the sparsified vector 𝒞(𝐞t+12,k)𝒞subscript𝐞𝑡12𝑘\mathcal{C}({\bf e}_{t+\frac{1}{2},k})caligraphic_C ( bold_e start_POSTSUBSCRIPT italic_t + divide start_ARG 1 end_ARG start_ARG 2 end_ARG , italic_k end_POSTSUBSCRIPT )... | C |
Olshausen et al. [43] presented an objective function that considers subjective measures of sparseness of the activation maps, however in this work we use the direct measure of compression ratio.
Previous work by [44] have used a weighted combination of the number of neurons, percentage root-mean-squared difference and... | The increased number of weights and non-zero activations make DNNs more complex, and thus more difficult to use in problems that require corresponding causality of the output with a specific set of neurons.
The majority of domains where machine learning is applied, including critical areas such as healthcare [26], requ... | A limitation of SANs is the use of varying amplitude-only kernels, which are not sufficient for more complex data and also do not fully utilize the compressibility of the data.
A possible solution would be using a grid sampler [45] on the kernel allowing it to learn more general transformations (such as scale) than sim... | It is interesting to note that in some cases SANs reconstructions, such as for the Extrema-Pool indices, performed even better than the original data.
This suggests the overwhelming presence of redundant information that resides in the raw pixels of the original data and further indicates that SANs extract the most rep... | The φ𝜑\varphiitalic_φ metric is also related to the rate-distortion theory [40], in which the maximum distortion is defined according to human perception, which however inevitably introduces a bias.
There is also relation with the field of Compressed Sensing [41] in which the sparsity of the data is exploited allowing... | B |
The essence of PBLLA is selecting an alternative UAV randomly in one iteration and improving its utility by altering power and altitude with a certain probability, which is determined by the utilities of two strategies and τ𝜏\tauitalic_τ. UAV prefers to select the power and altitude which provide higher utility. Neve... |
Since PBLLA only allows one single UAV to alter strategies in one iteration, such defect would cause computation time to grow exponentially in large-scale UAVs systems. In terms of large-scale UAVs ad-hoc networks with a number of UAVs denoted as M𝑀Mitalic_M, M2superscript𝑀2M^{2}italic_M start_POSTSUPERSCRIPT 2 end_... |
Compared with other algorithms, novel algorithm SPBLLA has more advantages in learning rate. Various algorithms have been employed in the UAV networks in search of the optimal channel selection [31][29], such as stochastic learning algorithm [30]. The most widely seen algorithm–LLA is an ideal method for NE approachin... | Fig. 15 presents the learning rate of PBLLA and SPBLLA when τ=0.01𝜏0.01\tau=0.01italic_τ = 0.01. As m𝑚mitalic_m increases the learning rate of SPBLLA decreases, which has been shown in Fig. 15. However, when m𝑚mitalic_m is small, SPBLLA’s learning rate is about 3 times that of PBLLA showing the great advantage of sy... |
The learning rate of the extant algorithm is also not desirable [13]. Recently, a new fast algorithm called binary log-linear learning algorithm (BLLA) has been proposed by [14]. However, in this algorithm, only one UAV is allowed to change strategy in one iteration based on current game state, and then another UAV ch... | A |
=ΣejBese3absentsubscript𝑒𝑗absentΣsuperscript𝐵𝑒superscript𝑠𝑒3\displaystyle=\overset{e_{j}}{\underset{}{\Sigma}}\,B^{e}\frac{s^{e}}{3}= start_OVERACCENT italic_e start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT end_OVERACCENT start_ARG start_UNDERACCENT end_UNDERACCENT start_ARG roman_Σ end_ARG end_ARG italic_B st... | U¯r′superscriptsubscript¯𝑈𝑟′\displaystyle\overline{U}_{r}^{\prime}over¯ start_ARG italic_U end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT
=Dr¯¯∗U¯absent¯¯𝐷𝑟¯𝑈\displaystyle=\overline{\overline{Dr}}*\overline{U}= over¯ start_ARG over¯ start_ARG italic_D italic_r e... | U^r′superscriptsubscript^𝑈𝑟′\displaystyle\widehat{U}_{r}^{\prime}over^ start_ARG italic_U end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT
=Dr^¯∗U¯absent¯^𝐷𝑟¯𝑈\displaystyle=\overline{\widehat{Dr}}*\overline{U}= over¯ start_ARG over^ start_ARG italic_D italic_r end... | =S¯¯−1∗(M^¯T∗S^^∗Dr^¯)absentsuperscript¯¯𝑆1superscript¯^𝑀𝑇^^𝑆¯^𝐷𝑟\displaystyle=\overline{\overline{S}}^{-1}*\left(\overline{\widehat{M}}^{T}*%
\widehat{\widehat{S}}*\overline{\widehat{Dr}}\right)= over¯ start_ARG over¯ start_ARG italic_S end_ARG end_ARG start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ∗ ( over¯ sta... | U¯r′superscriptsubscript¯𝑈𝑟′\displaystyle\overline{U}_{r}^{\prime}over¯ start_ARG italic_U end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT
=(S¯¯−1∗(M^¯T∗S^^∗Dr^¯))∗U¯absentsuperscript¯¯𝑆1superscript¯^𝑀𝑇^^𝑆¯^𝐷𝑟¯𝑈\displaystyle=\left(\overline{\overline{S}}^{-1}... | D |
When using the framework, one can further require reflexivity on the comparability functions, i.e. f(xA,xA)=1A𝑓subscript𝑥𝐴subscript𝑥𝐴subscript1𝐴f(x_{A},x_{A})=1_{A}italic_f ( italic_x start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT ) = 1 start_POSTSUBSCRIP... | Intuitively, if an abstract value xAsubscript𝑥𝐴x_{A}italic_x start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT of ℒAsubscriptℒ𝐴\mathcal{L}_{A}caligraphic_L start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT is interpreted as 1111 (i.e., equality)
by hAsubscriptℎ𝐴h_{A}italic_h start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT... | When using the framework, one can further require reflexivity on the comparability functions, i.e. f(xA,xA)=1A𝑓subscript𝑥𝐴subscript𝑥𝐴subscript1𝐴f(x_{A},x_{A})=1_{A}italic_f ( italic_x start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT ) = 1 start_POSTSUBSCRIP... | fA(u,v)=fB(u,v)={1if u=v≠nullaif u≠null,v≠null and u≠vbif u=v=null0otherwise.subscript𝑓𝐴𝑢𝑣subscript𝑓𝐵𝑢𝑣cases1if 𝑢𝑣null𝑎formulae-sequenceif 𝑢null𝑣null and 𝑢𝑣𝑏if 𝑢𝑣null0otherwise.f_{A}(u,v)=f_{B}(u,v)=\begin{cases}1&\text{if }u=v\neq\texttt{null}\\
a&\text{if }u\neq\texttt{null},v\neq\texttt{null}... | Indeed, in practice the meaning of the null value in the data should be explained by domain experts, along with recommendations on how to deal with it.
Moreover, since the null value indicates a missing value, relaxing reflexivity of comparability functions on null allows to consider absent values as possibly | D |
To that end, we ran Dropout-DQN and DQN on one of the classic control environments to express the effect of Dropout on Variance and the learned policies quality. For the Overestimation phenomena, we ran Dropout-DQN and DQN on a Gridworld environment to express the effect of Dropout because in such environment the optim... |
Reinforcement Learning (RL) is a learning paradigm that solves the problem of learning through interaction with environments, this is a totally different approach from the other learning paradigms that have been studied in the field of Machine Learning namely the supervised learning and the unsupervised learning. Rein... |
To evaluate the Dropout-DQN, we employ the standard reinforcement learning (RL) methodology, where the performance of the agent is assessed at the conclusion of the training epochs. Thus we ran ten consecutive learning trails and averaged them. We have evaluated Dropout-DQN algorithm on CARTPOLE problem from the Class... |
The sources of DQN variance are Approximation Gradient Error(AGE)[23] and Target Approximation Error(TAE)[24]. In Approximation Gradient Error, the error in gradient direction estimation of the cost function leads to inaccurate and extremely different predictions on the learning trajectory through different episodes b... | To that end, we ran Dropout-DQN and DQN on one of the classic control environments to express the effect of Dropout on Variance and the learned policies quality. For the Overestimation phenomena, we ran Dropout-DQN and DQN on a Gridworld environment to express the effect of Dropout because in such environment the optim... | B |
As one of the first high impact CNN-based segmentation models, Long et al. (2015) proposed fully convolutional networks for pixel-wise labeling. They proposed up-sampling (deconvolving) the output activation maps from which the pixel-wise output can be calculated. The overall architecture of the network is visualized ... |
As one of the first high impact CNN-based segmentation models, Long et al. (2015) proposed fully convolutional networks for pixel-wise labeling. They proposed up-sampling (deconvolving) the output activation maps from which the pixel-wise output can be calculated. The overall architecture of the network is visualized ... |
Several modified versions (e.g. deeper/shallower, adding extra attention blocks) of encoder-decoder networks have been applied to semantic segmentation (Amirul Islam et al., 2017; Fu et al., 2019b; Lin et al., 2017a; Peng et al., 2017; Pohlen et al., 2017; Wojna et al., 2017; Zhang et al., 2018d). Recently in 2018, De... |
In order to preserve the contextual spatial information within an image as the filtered input data progresses deeper into the network, Long et al. (2015) proposed to fuse the output with shallower layers’ output. The fusion step is visualized in Figure 4. | Vorontsov et al. (2019), using a dataset defined in Cohen et al. (2018), proposed an image-to-image based framework to transform an input image with object of interest (presence domain) like a tumor to an image without the tumor (absence domain) i.e. translate diseased image to healthy; next, their model learns to add ... | C |
Interestingly, the Dense architecture achieves the best performance on MUTAG, indicating that in this case, the connectivity of the graps does not carry useful information for the classification task.
The performance of the Flat baseline indicates that in Enzymes and COLLAB pooling operations are not necessary to impro... | Contrarily to graph classification, DiffPool and TopK𝐾Kitalic_K fail to solve this task and achieve an accuracy comparable to random guessing.
On the contrary, the topological pooling methods obtain an accuracy close to a classical CNN, with NDP significantly outperforming the other two techniques. |
When compared to other methods for graph pooling, NDP performs significantly better than other techniques that pre-compute the topology of the coarsened graphs, while it achieves a comparable performance with respect to state-of-the-art feature-based pooling methods. | In Fig. 7, we report the training time for the five different pooling methods.
As expected, GNNs configured with GRACLUS, NMF, and NDP are much faster to train compared to those based on DiffPool and TopK𝐾Kitalic_K, with NDP being slightly faster than the other two topological methods. | Figure 9: Example of coarsening on one graph from the Proteins dataset. In (a), the original adjacency matrix of the graph. In (b), (c), and (d) the edges of the Laplacians at coarsening level 0, 1, and 2, as obtained by the 3 different pooling methods GRACLUS, NMF, and the proposed NDP.
| C |
where wD∈ℝnTsuperscript𝑤𝐷superscriptℝsubscript𝑛𝑇w^{D}\in\mathbb{R}^{n_{T}}italic_w start_POSTSUPERSCRIPT italic_D end_POSTSUPERSCRIPT ∈ blackboard_R start_POSTSUPERSCRIPT italic_n start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT end_POSTSUPERSCRIPT. This optimization finds a weighting of the number of decision trees... |
The proposed method generates data from a random forest and trains a neural network that imitates the random forest. The goal is that the neural network approximates the same function as the random forest. This also implies that the network reaches the same accuracy if successful. | Our proposed approach, called Neural Random Forest Imitation (NRFI), implicitly transforms random forests into neural networks.
The main concept includes (1) generating training data from decision trees and random forests, (2) adding strategies for reducing conflicts and increasing the variety of the generated examples... | Finally, a neural network that imitates the random forest is trained. The network learns the decision boundaries from the generated data and approximates the same function as the random forest.
The network architecture is based on a fully connected network with one or multiple hidden layers. | NRFI with and without the original data is shown for different network architectures. The smallest architecture has 2222 neurons in both hidden layers and the largest 128128128128. For NRFI (gen-ori), we can see that a network with 16161616 neurons in both hidden layers (NN-16-16) is already sufficient to learn the dec... | C |
Coupled with powerful function approximators such as neural networks, policy optimization plays a key role in the tremendous empirical successes of deep reinforcement learning (Silver et al., 2016, 2017; Duan et al., 2016; OpenAI, 2019; Wang et al., 2018). In sharp contrast, the theoretical understandings of policy opt... |
A line of recent work (Fazel et al., 2018; Yang et al., 2019a; Abbasi-Yadkori et al., 2019a, b; Bhandari and Russo, 2019; Liu et al., 2019; Agarwal et al., 2019; Wang et al., 2019) answers the computational question affirmatively by proving that a wide variety of policy optimization algorithms, such as policy gradient... | Our work is based on the aforementioned line of recent work (Fazel et al., 2018; Yang et al., 2019a; Abbasi-Yadkori et al., 2019a, b; Bhandari and Russo, 2019; Liu et al., 2019; Agarwal et al., 2019; Wang et al., 2019) on the computational efficiency of policy optimization, which covers PG, NPG, TRPO, PPO, and AC. In p... | for any function f:𝒮→ℝ:𝑓→𝒮ℝf:{\mathcal{S}}\rightarrow\mathbb{R}italic_f : caligraphic_S → blackboard_R. By allowing the reward function to be adversarially chosen in each episode, our setting generalizes the stationary setting commonly adopted by the existing work on value-based reinforcement learning (Jaksch et al.... |
Broadly speaking, our work is related to a vast body of work on value-based reinforcement learning in tabular (Jaksch et al., 2010; Osband et al., 2014; Osband and Van Roy, 2016; Azar et al., 2017; Dann et al., 2017; Strehl et al., 2006; Jin et al., 2018) and linear settings (Yang and Wang, 2019b, a; Jin et al., 2019;... | A |
In experiments, we demonstrated on two benchmark data sets the difficulty of finding a good trade-off among prediction quality, representational efficiency and computational efficiency.
Considering three embedded hardware platforms, we showed that massive parallelism is required for inference efficiency and that quanti... | We furthermore point out that hardware properties and the corresponding computational efficiency form a large fraction of resource efficiency.
This highlights the need to consider particular hardware targets when searching for resource-efficient machine learning models. | In experiments, we demonstrated on two benchmark data sets the difficulty of finding a good trade-off among prediction quality, representational efficiency and computational efficiency.
Considering three embedded hardware platforms, we showed that massive parallelism is required for inference efficiency and that quanti... | The computational cost of performing inference should match the (usually limited) resources in deployed systems and exploit the available hardware optimally in terms of time and energy.
Computational efficiency, in particular, also includes mapping the representational efficiency to available hardware structures. | In this regard, resource-efficient neural networks for embedded systems are concerned with the trade-off between prediction quality and resource efficiency (i.e., representational efficiency and computational efficiency). This is highlighted in Figure 1.
Note that this requires observing overall constraints such as pre... | A |
In Section 7, we prove a number of results concerning the homotopy types of Vietoris-Rips filtrations of spheres and complex projective spaces. Also, we fully compute the homotopy types of Vietoris-Rips filtration of spheres with ℓ∞superscriptℓ\ell^{\infty}roman_ℓ start_POSTSUPERSCRIPT ∞ end_POSTSUPERSCRIPT-norm. | In Section 8, we reprove Rips and Gromov’s result about the contractibility of the Vietoris-Rips complex of hyperbolic geodesic metric spaces, by using our method consisting of isometric embeddings into injective metric spaces. As a result, we will be able to bound the length of intervals in Vietoris-Rips persistence b... | The simplicial complex nowadays referred to as the Vietoris-Rips complex was originally introduced by Leopold Vietoris in the early 1900s in order to build a homology theory for metric spaces [79]. Later, Eliyahu Rips and Mikhail Gromov [47] both utilized the Vietoris-Rips complex in their study of hyperbolic groups.
| Of central interest in topological data analysis has been the question of providing a complete characterization of the Vietoris-Rips persistence barcodes of spheres of different dimensions. Despite the existence of a complete answer to the question for the case of 𝕊1superscript𝕊1\mathbb{S}^{1}blackboard_S start_POSTS... |
In Section 7, we prove a number of results concerning the homotopy types of Vietoris-Rips filtrations of spheres and complex projective spaces. Also, we fully compute the homotopy types of Vietoris-Rips filtration of spheres with ℓ∞superscriptℓ\ell^{\infty}roman_ℓ start_POSTSUPERSCRIPT ∞ end_POSTSUPERSCRIPT-norm. | A |
One way to obtain an indication of a projection’s quality is to compute a single scalar value, equivalent to a final score. Examples are Normalized Stress [7], Trustworthiness and Continuity [24], and Distance Consistency (DSC) [25]. More recently, ClustMe [26] was proposed as a perception-based measure that ranks scat... | We present a Neighborhood Preservation plot (Figure 1(g)) that shows an overview of the preservation of neighborhoods of different sizes (k𝑘kitalic_k) in both the entire projection and the current selection, based on the Jaccard distance between sets:
| we present t-viSNE, a tool designed to support the interactive exploration of t-SNE projections (an extension to our previous poster abstract [17]). In contrast to other, more general approaches, t-viSNE was designed with the specific problems related to the investigation of t-SNE projections in mind, bringing to light... | The difference line plot (d), on the other hand, builds on the standard plot by highlighting the differences between the selection and the global average, shown as positive and negative values around the 0 value of the y-axis.
It provides a clearer overall picture of the difference in preservation among all the shown s... | As an example, the set difference from Martins et al. [33] uses the Jaccard set-distance between the two sets of neighbors of a point in low- and high-dimensional space in order to compute a measure of Neighborhood Preservation. We have chosen to adopt it in our work, in contrast to others, because of its intuitive int... | D |
Similarity in metaheuristics: A gentle step towards a comparison methodology - 2022 [27]: This paper uses a pool template as a framework for decomposing and analyzing metaheuristics, inspired by another previous work. This template works as a framework for decomposing and analyzing metaheuristics based on these concept... |
50 years of metaheuristics - 2024 [40]: This overview traces the last 50 years of the field, starting from the roots of the area to the latest proposals to hybridize metaheuristics with machine learning. The revision encompasses constructive (GRASP and ACO), local search (iterated local search, Tabu search, variable n... | Good practices for designing metaheuristics: It gathers several works that are guidelines for good practices related to research orientation to measure novelty [26], to measure similarity in metaheuristics [27], Metaheuristics “In the Large” (to support the development, analysis, and comparison of new approaches) [28],... | Metaheuristics “In the Large” - 2022 [28]: The objective of this work is to provide a useful tool for researchers. To address the lack of novelty, the authors propose a new infrastructure to support the development, analysis, and comparison of new approaches. This framework is based on (1) the use of algorithm template... |
The constant evolution of the field leads to a significant issue: the lack of novelty in metaheuristics. However, researchers recognize the need to address this problem and have proposed methods to evaluate the novelty of new algorithms. This section shows different studies and guidelines to measure novelty, to design... | C |
Figure 1: Framework of AdaGAE. k0subscript𝑘0k_{0}italic_k start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the initial sparsity. First, we construct a sparse graph via the generative model defined in Eq. (7). The learned graph is employed to apply the GAE designed for the weighted graphs. After training the GAE, we update ... | As well as the well-known k𝑘kitalic_k-means [1, 2, 3], graph-based clustering [4, 5, 6] is also a representative kind of clustering method.
Graph-based clustering methods can capture manifold information so that they are available for the non-Euclidean type data, which is not provided by k𝑘kitalic_k-means. Therefore,... | (1) Via extending the generative graph models into general type data, GAE is naturally employed as the basic representation learning model and weighted graphs can be further applied to GAE as well. The connectivity distributions given by the generative perspective also inspires us to devise a novel architecture for dec... |
In recent years, GCNs have been studied a lot to extend neural networks to graph type data. How to design a graph convolution operator is a key issue and has attracted a mass of attention. Most of them can be classified into 2 categories, spectral methods [24] and spatial methods[25]. | However, the existing methods are limited to graph type data while no graph is provided for general data clustering. Since a large proportion of clustering methods are based on the graph, it is reasonable to consider how to employ GCN to promote the performance of graph-based clustering methods.
In this paper, we propo... | D |
We also want to understand the types of networks that we could test via domains-wide scans. To derive the business types we use the PeeringDB. We classify the ASes according to the following business types: content, enterprise, Network Service Provider (NSP), Cable/DSL/ISP, non-profit, educational/research, route serve... | There is a strong correlation between the AS size and the enforcement of spoofing, see Figure 13. Essentially, the larger the AS, the higher the probability that our tools identify that it does not filter spoofed packets. The reason can be directly related to our methodologies and the design of our study: the larger th... |
SMap (The Spoofing Mapper). In this work we present the first Internet-wide scanner for networks that filter spoofed inbound packets, we call the Spoofing Mapper (SMap). We apply SMap for scanning ingress-filtering in more than 90% of the Autonomous Systems (ASes) in the Internet. The measurements with SMap show that ... |
Domain-scan and IPv4-scan both show that the number of spoofable ASes grows with the overall number of the ASes in the Internet, see Figure 1. Furthermore, there is a correlation between fraction of scanned domains and ASes. Essentially the more domains are scanned, the more ASes are covered, and more spoofable ASes a... | Identifying servers with global IPID counters. We send packets from two hosts (with different IP addresses) to a server on a tested network. We implemented probing over TCP SYN, ping and using requests/responses to Name servers and we apply the suitable test depending on the server that we identify on the tested networ... | A |
Machine learning applications frequently deal with data-generating processes that change over time. Applications in such nonstationary environments include power use forecasting, recommendation systems, and environmental sensors [9]. Semisupervised learning, which has received a lot of attention in the sensor communit... | Biology frequently deals with drift [16]. For instance olfactory systems are constantly adapting, predominantly through feedback mechanisms. This section details some such models from computer science and neuroscience [17]. One example is the KIII model, a dynamic network resembling the olfactory bulb and feedforward a... |
The purpose of this study was to demonstrate that explicit representation of context can allow a classification system to adapt to sensor drift. Several gas classifier models were placed in a setting with progressive sensor drift and were evaluated on samples from future contexts. This task reflects the practical goal... | While natural systems cope with changing environments and embodiments well, they form a serious challenge for artificial systems. For instance, to stay reliable over time, gas sensing systems must be continuously recalibrated to stay accurate in a changing physical environment. Drawing motivation from nature, this pape... |
One prominent feature of the mammalian olfactory system is feedback connections to the olfactory bulb from higher-level processing regions. Activity in the olfactory bulb is heavily influenced by behavioral and value-based information [19], and in fact, the bulb receives more neural projections from higher-level regio... | A |
The goal would be to obtain an algorithm with running time 2O(f(δ)n)superscript2𝑂𝑓𝛿𝑛2^{O(f(\delta)\sqrt{n})}2 start_POSTSUPERSCRIPT italic_O ( italic_f ( italic_δ ) square-root start_ARG italic_n end_ARG ) end_POSTSUPERSCRIPT, where f(n)=O(n1/6)𝑓𝑛𝑂superscript𝑛16f(n)=O(n^{1/6})italic_f ( italic_n ) = italic... | It would be interesting to see whether a direct proof can be given for this fundamental result.
We note that the proof of Theorem 2.1 can easily be adapted to point sets of which the x𝑥xitalic_x-coordinates of the points need not be integer, as long as the difference between x𝑥xitalic_x-coordinates of any two consecu... | First of all, the ΔisubscriptΔ𝑖\Delta_{i}roman_Δ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT are now independent.
Second, as we will prove next, the expected running time of an algorithm on a uniformly distributed point set can be bounded by the expected running time of that algorithm on a point set generated this ... | We believe that our algorithm can serve as the basis of an algorithm solving such a problem, under the assumption that the point sets are dense enough to ensure that the solution will generally follow these curves / segments. Making this precise, and investigating how the running time depends on the number of line segm... | In the second step, we therefore describe a method to generate the random point set in a different way, and we show how to relate the expected running times in these two settings.
In the third step, we will explain which changes are made to the algorithm. | C |
The problem of presenting (finitely generated) free groups and semigroups in a self-similar way has a long history [15]. A self-similar presentation in this context is typically a faithful action on an infinite regular tree (with finite degree) such that, for any element and any node in the tree, the action of the elem... |
There are quite a few results on free (and related) products of self-similar or automaton groups (again see [15] for an overview) but many of them present the product as a subgroup of an automaton/self-similar group and, thus, loose the self-similarity property. An exception here is a line of research based on the Bel... | The construction used to prove Theorem 6 can also be used to obtain results which are not immediate corollaries of the theorem (or its corollary for automaton semigroups in 8). As an example, we prove in the following theorem that it is possible to adjoin a free generator to every self-similar semigroup without losing ... |
There is a quite interesting evolution of constructions to present free groups in a self-similar way or even as automaton groups (see [15] for an overview). This culminated in constructions to present free groups of arbitrary rank as automaton groups where the number of states coincides with the rank [18, 17]. While t... | from one to the other, then their free product S⋆T⋆𝑆𝑇S\star Titalic_S ⋆ italic_T is an automaton semigroup (8). This is again a strict generalization of [19, Theorem 3.0.1] (even if we only consider complete automata).
Third, we show this result in the more general setting of self-similar semigroups111Note that the c... | C |
SCR divides the region proposals into influential and non-influential regions and penalizes the model if: 1) 𝒮(agt)𝒮subscript𝑎𝑔𝑡\mathcal{S}(a_{gt})caligraphic_S ( italic_a start_POSTSUBSCRIPT italic_g italic_t end_POSTSUBSCRIPT ) of a non-influential region is higher than an influential region, and 2) the regio... | Here, we study these methods. We find that their improved accuracy does not actually emerge from proper visual grounding, but from regularization effects, where the model forgets the linguistic priors in the train set, thereby performing better on the test set. To support these claims, we first show that it is possible... | We probe the reasons behind the performance improvements of HINT and SCR. We first analyze if the results improve even when the visual cues are irrelevant (Sec. 4.2) or random (Sec. 4.3) and examine if their differences are statistically significant (Sec. 4.4). Then, we analyze the regularization effects by evaluating ... | We test our regularization method on random subsets of varying sizes. Fig. A6 shows the results when we apply our loss to 1−100%1percent1001-100\%1 - 100 % of the training instances. Clearly, the ability to regularize the model does not vary much with respect to the size of the train subset, with the best performance o... | As observed by Selvaraju et al. (2019) and as shown in Fig. 2, we observe small improvements on VQAv2 when the models are fine-tuned on the entire train set. However, if we were to compare against the improvements in VQA-CPv2 in a fair manner, i.e., only use the instances with visual cues while fine-tuning, then, the p... | B |
To satisfy the need for a much larger corpus of privacy policies, we introduce the PrivaSeer Corpus of 1,005,380 English language website privacy policies. The number of unique websites represented in PrivaSeer is about ten times larger than the next largest public collection of web privacy policies Amos et al. (2020)... |
For the data practice classification task, we leveraged the OPP-115 Corpus introduced by Wilson et al. (2016). The OPP-115 Corpus contains manual annotations of 23K fine-grained data practices on 115 privacy policies annotated by legal experts. To the best of our knowledge, this is the most detailed and widely used da... |
Prior collections of privacy policy corpora have led to progress in privacy research. Wilson et al. (2016) released the OPP-115 Corpus, a dataset of 115 privacy policies with manual annotations of 23k fine-grained data practices, and they created a baseline for classifying privacy policy text into one of ten categorie... | Other corpora similar to OPP-115 Corpus have enabled research on privacy practices. The PrivacyQA corpus contains 1,750 questions and expert-annotated answers for the privacy question answering task (Ravichander et al., 2019). Similarly, Lebanoff and Liu (2018) constructed the first corpus of human-annotated vague word... |
Natural language processing (NLP) provides an opportunity to automate the extraction of salient details from privacy policies, thereby reducing human effort and enabling the creation of tools for internet users to understand and control their online privacy. Existing research has achieved some success using expert ann... | B |
Figure 1: Knowledge generation model for ensemble learning with VA derived from the model by Sacha et al. [44]. On the left, it illustrates how a VA system can enable the exploration of the data and the models with the use of visualization. On the right, a number of design goals assist the human in the exploration, ve... | In a bucket of models, the best model for a specific problem is automatically chosen from a set of available options. This strategy is conceptually different to the ideas of bagging, boosting, and stacking, but still related to ensemble learning.
Chen et al. [6] utilize a bucket of latent Dirichlet allocation (LDA) mod... | The rest of this paper is organized as follows. In the next section, we discuss the literature related to visualization of ensemble learning.
Afterwards, we describe the knowledge generation model for ensemble learning with VA, design goals, and analytical tasks for attaching VA to ensemble learning. | Visualization systems have been developed for the exploration of diverse aspects of bagging, boosting, and further strategies such as “bucket of models”.
Stacking, however, has so far not received comparable attention by the InfoVis/VA communities: actually, we have not found any literature describing the construction ... |
Figure 1: Knowledge generation model for ensemble learning with VA derived from the model by Sacha et al. [44]. On the left, it illustrates how a VA system can enable the exploration of the data and the models with the use of visualization. On the right, a number of design goals assist the human in the exploration, ve... | C |
We thus have 3333 cases, depending on the value of the tuple
(p(v,[010]),p(v,[323]),p(v,[313]),p(v,[003]))𝑝𝑣delimited-[]010𝑝𝑣delimited-[]323𝑝𝑣delimited-[]313𝑝𝑣delimited-[]003(p(v,[010]),p(v,[323]),p(v,[313]),p(v,[003]))( italic_p ( italic_v , [ 010 ] ) , italic_p ( italic_v , [ 323 ] ) , italic_p ( italic_v... | Then, by using the adjacency of (v,[013])𝑣delimited-[]013(v,[013])( italic_v , [ 013 ] ) with each of
(v,[010])𝑣delimited-[]010(v,[010])( italic_v , [ 010 ] ), (v,[323])𝑣delimited-[]323(v,[323])( italic_v , [ 323 ] ), and (v,[112])𝑣delimited-[]112(v,[112])( italic_v , [ 112 ] ), we can confirm that | By using the pairwise adjacency of (v,[112])𝑣delimited-[]112(v,[112])( italic_v , [ 112 ] ), (v,[003])𝑣delimited-[]003(v,[003])( italic_v , [ 003 ] ), and
(v,[113])𝑣delimited-[]113(v,[113])( italic_v , [ 113 ] ), we can confirm that in the 3333 cases, these | {0¯,1¯,2¯,3¯,[013],[010],[323],[313],[112],[003],[113]}.¯0¯1¯2¯3delimited-[]013delimited-[]010delimited-[]323delimited-[]313delimited-[]112delimited-[]003delimited-[]113\{\overline{0},\overline{1},\overline{2},\overline{3},[013],[010],[323],[313],%
[112],[003],[113]\}.{ over¯ start_ARG 0 end_ARG , over¯ start_ARG 1 end... | p(v,[013])=p(v,[313])=p(v,[113])=1𝑝𝑣delimited-[]013𝑝𝑣delimited-[]313𝑝𝑣delimited-[]1131p(v,[013])=p(v,[313])=p(v,[113])=1italic_p ( italic_v , [ 013 ] ) = italic_p ( italic_v , [ 313 ] ) = italic_p ( italic_v , [ 113 ] ) = 1.
Similarly, when f=[112]𝑓delimited-[]112f=[112]italic_f = [ 112 ], | B |
When applying MAML to NLP, several factors can influence the training strategy and performance of the model. Firstly, the data quantity within the datasets used as ”tasks” varies across different applications, which can impact the effectiveness of MAML [Serban et al., 2015, Song et al., 2020]. Secondly, while vanilla ... | In this paper, we take an empirical approach to systematically investigating these impacting factors and finding when MAML works the best. We conduct extensive experiments over 4 datasets. We first study the effects of data quantity and distribution on the training strategy:
RQ1. Since the parameter initialization lear... |
To answer RQ1, we compare the changing trend of the general language model and the task-specific adaptation ability during the training of MAML to find whether there is a trade-off problem. (Figure 1) We select the trained parameter initialization at different MAML training epochs and evaluate them directly on the met... | The finding suggests that parameter initialization at the late training stage has strong general language generation ability, but performs comparative poorly in task-specific adaptation.
Although in the early training stage, the performance improves benefiting from the pre-trained general language model, if the languag... |
When applying MAML to NLP, several factors can influence the training strategy and performance of the model. Firstly, the data quantity within the datasets used as ”tasks” varies across different applications, which can impact the effectiveness of MAML [Serban et al., 2015, Song et al., 2020]. Secondly, while vanilla ... | A |
In this paper, we consider a dynamic mission-driven UAV network with UAV-to-UAV mmWave communications, wherein multiple transmitting UAVs (t-UAVs) simultaneously transmit to a receiving UAV (r-UAV). In such a scenario, we focus on inter-UAV communications in UAV networks, and the UAV-to-ground communications are not in... |
The first study on the beam tracking framework for CA-enabled UAV mmWave networks. We propose an overall beam tracking framework to exemplify the idea of the DRE-covered CCA integrated with UAVs, and reveal that CA can offer full-spatial coverage and facilitate beam tracking, thus enabling high-throughput inter-UAV da... |
The specialized codebook design of the DRE-covered CCA for multi-UAV mobile mmWave communications. Under the guidance of the proposed framework, a novel hierarchical codebook is designed to encompass both the subarray patterns and beam patterns. The newly proposed CA codebook can fully exploit the potentials of the DR... |
When considering UAV communications with UPA or ULA, a UAV is typically modeled as a point in space without considering its size and shape. Actually, the size and shape can be utilized to support more powerful and effective antenna array. Inspired by this basic consideration, the conformal array (CA) [16] is introduce... | For both static and mobile mmWave networks, codebook design is of vital importance to empower the feasible beam tracking and drive the mmWave antenna array for reliable communications [22, 23]. Recently, ULA/UPA-oriented codebook designs have been proposed for mmWave networks, which include the codebook-based beam trac... | A |
Thus,
a¯|b¯conditional¯𝑎¯𝑏\bar{a}|\bar{b}over¯ start_ARG italic_a end_ARG | over¯ start_ARG italic_b end_ARG-regular digraphs with size M¯¯𝑀\bar{M}over¯ start_ARG italic_M end_ARG can be characterized as a¯|b¯conditional¯𝑎¯𝑏\bar{a}|\bar{b}over¯ start_ARG italic_a end_ARG | over¯ start_ARG italic_b end_ARG-biregula... | We start in this section by giving proofs only for the 1111-color case, without the completeness requirement. While this case does not directly correspond to any formula used in the proof of Theorem 3.7 (since matrices (4) have 2 rows even when there are no binary predicates), this case gives the flavor of the argument... | The case of fixed degree and multiple colors is done via an induction, using merging and then swapping to eliminate parallel edges.
The case of unfixed degree is handled using a case analysis depending on whether sizes are “big enough”, but the approach is different from | This will be bootstrapped to the multi-color case in later sections. Note that the 1111-color case with the completeness requirement is not very interesting, and also not useful for the general case: completeness states that every node on
the left must be connected, via the unique edge relation, to every node on the ri... | To conclude this section, we stress that although the 1111-color case contains many of the key ideas, the multi-color case requires a finer
analysis to deal with the “big enough” case, and also may benefit from a reduction that allows one to restrict | D |
In this paper, we study temporal-difference (TD) (Sutton, 1988) and Q-learning (Watkins and Dayan, 1992), two of the most prominent algorithms in deep reinforcement learning, which are further connected to policy gradient (Williams, 1992) through its equivalence to soft Q-learning (O’Donoghue et al., 2016; Schulman et... |
Contribution. Going beyond the NTK regime, we prove that, when the value function approximator is an overparameterized two-layer neural network, TD and Q-learning globally minimize the mean-squared projected Bellman error (MSPBE) at a sublinear rate. Moreover, in contrast to the NTK regime, the induced feature represe... | Szepesvári, 2018; Dalal et al., 2018; Srikant and Ying, 2019) settings. See Dann et al. (2014) for a detailed survey. Also, when the value function approximator is linear, Melo et al. (2008); Zou et al. (2019); Chen et al. (2019b) study the convergence of Q-learning. When the value function approximator is nonlinear, T... |
corresponding to θ(m)(k)=(θ1(k),…,θm(k))∈ℝD×msuperscript𝜃𝑚𝑘subscript𝜃1𝑘…subscript𝜃𝑚𝑘superscriptℝ𝐷𝑚\theta^{(m)}(k)=(\theta_{1}(k),\ldots,\theta_{m}(k))\in\mathbb{R}^{D\times m}italic_θ start_POSTSUPERSCRIPT ( italic_m ) end_POSTSUPERSCRIPT ( italic_k ) = ( italic_θ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT (... | To address such an issue of divergence, nonlinear gradient TD (Bhatnagar et al., 2009) explicitly linearizes the value function approximator locally at each iteration, that is, using its gradient with respect to the parameter as an evolving feature representation. Although nonlinear gradient TD converges, it is unclear... | D |
Table 4 shows that, even though this is counter-intuitive, element-wise addition (with fewer parameters) empirically results in slightly higher BLEU than the concatenation operation. Furthermore, even though using 2 depth-wise LSTM sub-layers connecting cross- and masked self-attention sub-layers leads to the highest ... | Directly replacing residual connections with LSTM units will introduce a large amount of additional parameters and computation. Given that the task of computing the LSTM hidden state is similar to the feed-forward sub-layer in the original Transformer layers, we propose to replace the feed-forward sub-layer with the ne... |
Table 5 shows that: 1) Sharing parameters for the computation (Equation 6) of the depth-wise LSTM hidden state significantly hampers performance, which is consistent with our conjecture. 2) Sharing parameters for the computation of gates (Equations 2, 3, 4) leads to slightly higher BLEU with fewer parameters introduce... |
In our approach (“with depth-wise LSTM”), we used the 2-layer neural network for the computation of the LSTM hidden state (Equation 6) and shared LSTM parameters across stacked encoder layers and different shared parameters across decoder layers for computing the LSTM gates (Equations 2, 3, 4). Details are provided in... | As the number of Transformer layers is pre-specified, the parameters of the depth-wise LSTM can either be shared across layers or be independent. Table 3 documents the importance of the capacity of the module for the hidden state computation, and sharing the module is likely to hurt its capacity. We additionally study ... | D |
the corresponding Alexandroff topologies:
X≜⟨X,τ→,𝖥𝖮[σ]⟩≜𝑋𝑋subscriptτ→𝖥𝖮delimited-[]σX\triangleq\left\langle X,\uptau_{\to},\mathsf{FO}[\upsigma]\right\rangleitalic_X ≜ ⟨ italic_X , roman_τ start_POSTSUBSCRIPT → end_POSTSUBSCRIPT , sansserif_FO [ roman_σ ] ⟩ and for n∈ℕ𝑛ℕn\in\mathbb{N}italic_n ∈ blackboard_N, l... | For A∈Fin(σ)𝐴FinσA\in\operatorname{Fin}(\upsigma)italic_A ∈ roman_Fin ( roman_σ ) and n≥1𝑛1n\geq 1italic_n ≥ 1, there exists a structure
Coren(A)superscriptCore𝑛𝐴\operatorname{Core}^{n}(A)roman_Core start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT ( italic_A ) of tree-depth at most n𝑛nitalic_n such that | A→nCoren(A)subscript→𝑛𝐴superscriptCore𝑛𝐴A\to_{n}\operatorname{Core}^{n}(A)italic_A → start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT roman_Core start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT ( italic_A ), Coren(A)→nAsubscript→𝑛superscriptCore𝑛𝐴𝐴\operatorname{Core}^{n}(A)\to_{n}Aroman_Core start_POSTSUPERSC... | For all A∈Fin(σ)𝐴FinσA\in\operatorname{Fin}(\upsigma)italic_A ∈ roman_Fin ( roman_σ ), let ψA𝖤𝖥𝖮superscriptsubscript𝜓𝐴𝖤𝖥𝖮\psi_{A}^{\mathsf{EFO}}italic_ψ start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT start_POSTSUPERSCRIPT sansserif_EFO end_POSTSUPERSCRIPT be the
diagram sentence such that ⟦ψA𝖤𝖥𝖮⟧Struct(σ)... | all n≥1𝑛1n\geq 1italic_n ≥ 1, if A∈X𝐴𝑋A\in Xitalic_A ∈ italic_X then Coren(A)∈XsuperscriptCore𝑛𝐴𝑋\operatorname{Core}^{n}(A)\in Xroman_Core start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT ( italic_A ) ∈ italic_X since X𝑋Xitalic_X is
downwards closed. | A |
Qualitative Comparison: To qualitatively show the performance of different learning representations, we visualize the 3D distortion distribution maps (3D DDM) derived from the ground truth and these two schemes in Fig. 8, in which each pixel value of the distortion distribution map represents the distortion level. Sinc... |
Figure 11: Qualitative evaluations of the rectified distorted images on indoor (left) and outdoor (right) scenes. For each evaluation, we show the distorted image, ground truth, and corrected results of the compared methods: Alemán-Flores [23], Santana-Cedrés [24], Rong [8], Li [11], and Liao [12], and rectified resul... | We visually compare the corrected results from our approach with state-of-the-art methods using our synthetic test set and the real distorted images. To show the comprehensive rectification performance under different scenes, we split the test set into four types of scenes: indoor, outdoor, people, and challenging scen... | Figure 12: Qualitative evaluations of the rectified distorted images on people (left) and challenging (right) scenes. For each evaluation, we show the distorted image, ground truth, and corrected results of the compared methods: Alemán-Flores [23], Santana-Cedrés [24], Rong [8], Li [11], and Liao [12], and rectified re... | Figure 13: Qualitative evaluations of the rectified distorted images on real-world scenes. For each evaluation, we show the distorted image and corrected results of the compared methods: Alemán-Flores [23], Santana-Cedrés [24], Rong [8], Li [11], and Liao [12], and rectified results of our proposed approach, from left ... | A |
Apart from these empirical findings, there have been some theoretical
studies on large-batch training. For example, the convergence analyses of LARS have been reported in [34]. The work in [37] analyzed the inconsistency bias in decentralized momentum SGD and proposed DecentLaM for decentralized large-batch training. | We don’t use training tricks such as warm-up [7]. We adopt the linear learning rate decay strategy as default in the Transformers framework.
Table 5 shows the test accuracy results of the methods with different batch sizes. SNGM achieves the best performance for almost all batch size settings. | Figure 2 shows the learning curves of the five methods. We can observe that in the small-batch training, SNGM and other large-batch training methods achieve similar performance in terms of training loss and test accuracy as MSGD.
In large-batch training, SNGM achieves better training loss and test accuracy than the fou... | Furthermore, researchers in [19] argued that the extrapolation technique is suitable for large-batch training and proposed EXTRAP-SGD.
However, experimental implementations of these methods still require additional training tricks, such as warm-up, which may make the results inconsistent with the theory. | Many methods have been proposed for improving the performance of SGD with large batch sizes. The works in [7, 33]
proposed several tricks, such as warm-up and learning rate scaling schemes, to bridge the generalization gap under large-batch training settings. Researchers in [11] | C |
{\mathcal{F}}roman_support ( caligraphic_D ) ⊆ 2 start_POSTSUPERSCRIPT caligraphic_C end_POSTSUPERSCRIPT × blackboard_R start_POSTSUPERSCRIPT caligraphic_F end_POSTSUPERSCRIPT and, in the black-box setting, |𝒟|𝒟|\mathcal{D}|| caligraphic_D | may be uncountably infinite.
| The most general way to represent the scenario distribution 𝒟𝒟\mathcal{D}caligraphic_D is the black-box model [24, 12, 22, 19, 25], where we have access to an oracle to sample scenarios A𝐴Aitalic_A according to 𝒟𝒟\mathcal{D}caligraphic_D. We also consider the polynomial-scenarios model [23, 15, 21, 10], where the ... | Clustering is a fundamental task in unsupervised and self-supervised learning. The stochastic setting models situations in which decisions must be made in the presence of uncertainty and are of particular interest in learning and data science. The black-box model is motivated by data-driven applications where specific ... | The other three results are based on a reduction to a single-stage, deterministic robust outliers problem described in Section 4; namely, convert any ρ𝜌\rhoitalic_ρ-approximation algorithm for the robust outlier problem into a (ρ+2)𝜌2(\rho+2)( italic_ρ + 2 )-approximation algorithm for the corresponding two-stage sto... | Stochastic optimization, first introduced in the work of Beale [4] and Dantzig [8], provides a way to model uncertainty in the realization of the input data. In this paper, we give approximation algorithms for a family of problems in stochastic optimization, and more precisely in the 2222-stage recourse model [27].
Our... | B |
Both (sub)gradient noises and random graphs are considered in [11]-[13]. In [11], the local gradient noises are independent with bounded second-order moments and the graph sequence is i.i.d.
In [12]-[14], the (sub)gradient measurement noises are martingale difference sequences and their second-order conditional moments... | I. The local cost functions in this paper are not required to be differentiable and the subgradients only satisfy the linear growth condition.
The inner product of the subgradients and the error between local optimizers’ states and the global optimal solution inevitably exists in the recursive inequality of the conditi... | such as the economic dispatch in power grids ([1]) and the traffic flow control in intelligent transportation networks ([2]), et al. Considering the various uncertainties in practical network environments, distributed stochastic optimization algorithms have been widely studied. The (sub)gradients of local cost function... |
Motivated by distributed statistical learning over uncertain communication networks, we study the distributed stochastic convex optimization by networked local optimizers to cooperatively minimize a sum of local convex cost functions. The network is modeled by a sequence of time-varying random digraphs which may be sp... | In addition to uncertainties in information exchange, different assumptions on the cost functions have been discussed.
In the most of existing works on the distributed convex optimization, it is assumed that the subgradients are bounded if the local cost | D |
Typically, the attributes in microdata can be divided into three categories: (1) Explicit-Identifier (EI, also known as Personally-Identifiable Information), such as name and social security number, which can uniquely or mostly identify the record owner; (2) Quasi-Identifier (QI), such as age, gender and zip code, whi... | Specifically, there are three main steps in the proposed approach. First, MuCo partitions the tuples into groups and assigns similar records into the same group as far as possible. Second, the random output tables, which control the distribution of random output values within each group, are calculated to make similar ... | Generalization [8, 26] is one of the most widely used privacy-preserving techniques. It transforms the values on QI attributes into general forms, and the tuples with equally generalized values constitute an equivalence group. In this way, records in the same equivalence group are indistinguishable. k𝑘kitalic_k-Anonym... | However, despite protecting against both identity disclosure and attribute disclosure, the information loss of generalized table cannot be ignored. On the one hand, the generalized values are determined by only the maximum and the minimum QI values in equivalence groups, causing that the equivalence groups only preserv... |
Although the generalization for k𝑘kitalic_k-anonymity provides enough protection for identities, it is vulnerable to the attribute disclosure [23]. For instance, in Figure 1(b), the sensitive values in the third equivalence group are both “pneumonia”. Therefore, an adversary can infer the disease value of Dave by mat... | B |
In this section, we introduce our practice on three competitive segmentation methods including HTC, SOLOv2 and PointRend. We show step-by-step modifications adopted on PointRend, which achieves better performance and outputs much smoother instance boundaries than other methods.
| Deep learning has achieved great success in recent years Fan et al. (2019); Zhu et al. (2019); Luo et al. (2021, 2023); Chen et al. (2021). Recently, many modern instance segmentation approaches demonstrate outstanding performance on COCO and LVIS, such as HTC Chen et al. (2019a), SOLOv2 Wang et al. (2020), and PointRe... | Bells and Whistles. MaskRCNN-ResNet50 is used as baseline and it achieves 53.2 mAP. For PointRend, we follow the same setting as Kirillov et al. (2020) except for extracting both coarse and fine-grained features from the P2-P5 levels of FPN, rather than only P2 described in the paper. Surprisingly, PointRend yields 62.... | HTC is known as a competitive method for COCO and OpenImage. By enlarging the RoI size of both box and mask branches to 12 and 32 respectively for all three stages, we gain roughly 4 mAP improvement against the default settings in original paper. Mask scoring head Huang et al. (2019) adopted on the third stage gains an... |
Due to limited mask representation of HTC, we move on to SOLOv2, which utilizes much larger mask to segment objects. It builds an efficient yet simple instance segmentation framework, outperforming other segmentation methods like TensorMask Chen et al. (2019c), CondInst Tian et al. (2020) and BlendMask Chen et al. (20... | C |
For the significance of this conjecture we refer to the original paper [FK], and to Kalai’s blog [K] (embedded in Tao’s blog) which reports on all significant results concerning the conjecture. [KKLMS] establishes a weaker version of the conjecture. Its introduction is also a good source of information on the problem.
| We denote by εi:{−1,1}n→{−1,1}:subscript𝜀𝑖→superscript11𝑛11\varepsilon_{i}:\{-1,1\}^{n}\to\{-1,1\}italic_ε start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT : { - 1 , 1 } start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT → { - 1 , 1 } the projection onto the i𝑖iitalic_i-s coordinate: εi(δ1,…,δn)=δisubscript𝜀𝑖subsc... |
Here we give an embarrassingly simple presentation of an example of such a function (although it can be shown to be a version of the example in the previous version of this note). As was written in the previous version, an anonymous referee of version 1 wrote that the theorem was known to experts but not published. Ma... |
In version 1 of this note, which can still be found on the ArXiv, we showed that the analogous version of the conjecture for complex functions on {−1,1}nsuperscript11𝑛\{-1,1\}^{n}{ - 1 , 1 } start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT which have modulus 1111 fails. This solves a question raised by Gady Kozma s... | For the significance of this conjecture we refer to the original paper [FK], and to Kalai’s blog [K] (embedded in Tao’s blog) which reports on all significant results concerning the conjecture. [KKLMS] establishes a weaker version of the conjecture. Its introduction is also a good source of information on the problem.
| C |
Figure 1: Comparisons of different methods on cumulative reward under two different environments. The results are averaged over 10 trials and the error bars show the standard deviations. The environment changes abruptly in the left subfigure, whereas the environment changes gradually in the right subfigure. | For the case when the environment changes abruptly L𝐿Litalic_L times, our algorithm enjoys an O~(L1/3T2/3)~𝑂superscript𝐿13superscript𝑇23\tilde{O}(L^{1/3}T^{2/3})over~ start_ARG italic_O end_ARG ( italic_L start_POSTSUPERSCRIPT 1 / 3 end_POSTSUPERSCRIPT italic_T start_POSTSUPERSCRIPT 2 / 3 end_POSTSUPERSCRIPT ) dy... |
Figure 2 shows that the running times of LSVI-UCB-Restart and Ada-LSVI-UCB-Restart are roughly the same. They are much less compared with MASTER, OPT-WLSVI, LSVI-UCB, Epsilon-Greedy. This is because LSVI-UCB-Restart and Ada-LSVI-UCB-Restart can automatically restart according to the variation of the environment and th... | From Figure 1, we find that the restart strategy works better under abrupt changes than under gradual changes, since the gap between our algorithms and the baseline algorithms designed for stationary environments is larger in this setting. The reason is that the algorithms designed to explore in stationary MDPs are gen... | From Figure 1, we see LSVI-UCB-Restart with the knowledge of global variation drastically outperforms all other methods designed for stationary environments , in both abruptly-changing and gradually-changing environments, since it restarts the estimation of the Q𝑄Qitalic_Q function with knowledge of the total variatio... | C |
There is a very strong, negative correlation between the media sources of fake news and the level of trust in them (ref. Figures 1 and 2) which is statistically significant (r(9)=−0.81𝑟90.81r(9)=-0.81italic_r ( 9 ) = - 0.81, p<.005𝑝.005p<.005italic_p < .005). Trust is built on transparency and truthfulness, and t... | Singapore is a city-state with an open economy and diverse population that shapes it to be an attractive and vulnerable target for fake news campaigns (Lim, 2019). As a measure against fake news, the Protection from Online Falsehoods and Manipulation Act (POFMA) was passed on May 8, 2019, to empower the Singapore Gover... |
There is a very strong, negative correlation between the media sources of fake news and the level of trust in them (ref. Figures 1 and 2) which is statistically significant (r(9)=−0.81𝑟90.81r(9)=-0.81italic_r ( 9 ) = - 0.81, p<.005𝑝.005p<.005italic_p < .005). Trust is built on transparency and truthfulness, and t... |
In general, respondents possess a competent level of digital literacy skills with a majority exercising good news sharing practices. They actively verify news before sharing by checking with multiple sources found through the search engine and with authoritative information found in government communication platforms,... | While fake news is not a new phenomenon, the 2016 US presidential election brought the issue to immediate global attention with the discovery that fake news campaigns on social media had been made to influence the election (Allcott and Gentzkow, 2017). The creation and dissemination of fake news is motivated by politic... | C |
Consider the instance of encoding the relational information of the entity W3C into an embedding. All relevant information is structured in the form of triplets, such as (RDF,developer,W3C)RDFdeveloperW3C(\textit{RDF},\textit{developer},\textit{W3C})( RDF , developer , W3C ). Removing the self-entity W3C does not comp... |
Now, let’s consider a scenario where DAN is responsible for generating embeddings for the neighbors of W3C, specifically 𝐠Tim Berners-Leesubscript𝐠Tim Berners-Lee\mathbf{g}_{\text{Tim Berners-Lee}}bold_g start_POSTSUBSCRIPT Tim Berners-Lee end_POSTSUBSCRIPT, 𝐠RDFsubscript𝐠RDF\mathbf{g}_{\text{RDF}}bold_g start_POS... | Drawing inspiration from the CBOW schema, we propose Decentralized Attention Network (DAN) to distribute the relational information of an entity exclusively over its neighbors.
DAN retains complete relational information and empowers the induction of embeddings for new entities. For example, if W3C is a new entity, its... | Although 𝐞W3Csubscript𝐞W3C{\mathbf{e}}_{\text{W3C}}bold_e start_POSTSUBSCRIPT W3C end_POSTSUBSCRIPT dose not directly contribute to its output embedding 𝐠W3Csubscript𝐠W3C{\mathbf{g}}_{\text{W3C}}bold_g start_POSTSUBSCRIPT W3C end_POSTSUBSCRIPT, it plays a pivotal role in learning the embeddings of its neighbors, su... | To gain a deeper understanding of self-distillation, it is essential to analyze the relationship between the input embedding and the decentralized output embedding. Let’s consider the example of the entity W3C, denoted as 𝐞W3Csubscript𝐞W3C\mathbf{e}_{\text{W3C}}bold_e start_POSTSUBSCRIPT W3C end_POSTSUBSCRIPT for the... | B |
To evaluate the adaptability, we further adopt the policies learned from the Level 1111 to other levels. More specifically, for each method, we first save the last policy when training in the Level 1111, and then fine-tune such a policy in the Levels 2222 and 3333. Since the VDM and RFM methods perform the best in the ... | To further investigate the capability of our method in coping with highly stochastic environments, we conduct experiments on games where both the agent and its opponent are controlled by self-supervised exploratory policies. The stochasticity of the transition dynamics is much higher for both sides of the game since th... |
We illustrate the results in Fig. 9. We observe that the episode length becomes longer over training time with the intrinsic reward estimated from VDM, as anticipated. We observe that our method reaches the episode length of 104superscript10410^{4}10 start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT with the minimum iterati... | We observe that our method performs the best in most of the games, in both the sample efficiency and the performance of the best policy. The reason our method outperforms other baselines is the multimodality in dynamics that the Atari games usually have. Such multimodality is typically caused by other objects that are ... |
The complete procedure of self-supervised exploration with VDM is summarized in Algorithm 1. In each episode, the agent interacts with the environment to collect the transition st,at,st+1subscript𝑠𝑡subscript𝑎𝑡subscript𝑠𝑡1s_{t},a_{t},s_{t+1}italic_s start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT , italic_a start_... | A |
If we would add nodes to make the grid symmetric or tensorial, then
the number of nodes of the resulting (sparse) tensorial grid would scale exponentially 𝒪(nm)𝒪superscript𝑛𝑚\mathcal{O}(n^{m})caligraphic_O ( italic_n start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT ) with space dimension m∈ℕ𝑚ℕm\in\mathbb{N}ital... | We complement the established notion of unisolvent nodes by the dual notion of unisolvence. That is: For given arbitrary nodes P𝑃Pitalic_P, determine the polynomial space ΠΠ\Piroman_Π such that
P𝑃Pitalic_P is unisolvent with respect to ΠΠ\Piroman_Π. In doing so, we revisit earlier results by Carl de Boor and Amon Ros... | for a given polynomial space ΠΠ\Piroman_Π and a set of nodes P⊆ℝm𝑃superscriptℝ𝑚P\subseteq\mathbb{R}^{m}italic_P ⊆ blackboard_R start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT that is not unisolvent with respect to ΠΠ\Piroman_Π,
find a maximum subset P0⊆Psubscript𝑃0𝑃P_{0}\subseteq Pitalic_P start_POSTSUBSCRIPT 0 ... |
We realize the algorithm of Carl de Boor and Amon Ros [28, 29] in terms of Corollary 6.5 in case of the torus M=𝕋R,r2𝑀subscriptsuperscript𝕋2𝑅𝑟M=\mathbb{T}^{2}_{R,r}italic_M = blackboard_T start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_R , italic_r end_POSTSUBSCRIPT. That is, we consider | Here, we answer Questions 1–2.
To do so, we generalize the notion of unisolvent nodes PAsubscript𝑃𝐴P_{A}italic_P start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT, A⊆ℕm𝐴superscriptℕ𝑚A\subseteq\mathbb{N}^{m}italic_A ⊆ blackboard_N start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT to non-tensorial grids. This allows us... | A |
In the second case, the distributions μ𝜇\muitalic_μ and ν𝜈\nuitalic_ν are both d𝑑ditalic_d-dimensional Gaussian distributions with the same mean vector but different covariance metrics, where d∈{30,60}𝑑3060d\in\{30,60\}italic_d ∈ { 30 , 60 }.
More specifically, μ=𝒩(0,Id)𝜇𝒩0subscript𝐼𝑑\mu=\mathcal{N}(0,I_{d})i... | Several data-efficient two-sample tests [20, 21, 22] are constructed based on Maximum Mean Discrepancy (MMD), which quantifies the distance between two distributions by introducing test functions in a Reproducing Kernel Hilbert Space (RKHS).
However, it is pointed out in [23] that when the bandwidth is chosen based on ... | However, the two-sample tests based on concentration inequalities in Section III give conservative results in practice. We examine the two-sample tests using the projected Wasserstein distance via the permutation approach.
Specifically, we permute the collected data points for Np=100subscript𝑁𝑝100N_{p}=100italic_N st... | In other words, we only scale the first two diagonal entries in the covariance matrix of ν𝜈\nuitalic_ν to make the hypothesis testing problem difficult to perform.
We compare the performance of the PW test with the MMD test discussed in [20], where the kernel function is chosen to be the standard Gaussian kernel with ... | The last two plots correspond to covariance-shifted Gaussian distributions, where Fig. 1c) examines the power for different n𝑛nitalic_n with fixed d=60𝑑60d=60italic_d = 60, and Fig. 1d) examines the power for different d𝑑ditalic_d with fixed n=75𝑛75n=75italic_n = 75.
We can see that the power of all methods increas... | C |
VAE-type DGMs use amortized variational inference to learn an approximate posterior qϕ(H|x)subscript𝑞italic-ϕconditional𝐻𝑥q_{\phi}(H|x)italic_q start_POSTSUBSCRIPT italic_ϕ end_POSTSUBSCRIPT ( italic_H | italic_x ) by maximizing an evidence lowerbound (ELBO) to the log-marginal likelihood of the data under the mod... |
The model has two parts. First, we apply a DGM to learn only the disentangled part, C𝐶Citalic_C, of the latent space. We do that by applying any of the above mentioned VAEs111In this exposition we use unspervised trained VAEs as our base models but the framework also works with GAN-based or FLOW-based DGMs, supervise... | Amortization of the inference is achieved by parameterising the variational posterior with another deep neural network (called the encoder or the inference network) that outputs the variational posterior parameters as a function of X𝑋Xitalic_X. Thus, after jointly training the encoder and decoder, a VAE model can perf... | Specifically, we apply a DGM to learn the nuisance variables Z𝑍Zitalic_Z, conditioned on the output image of the first part, and use Z𝑍Zitalic_Z in the normalization layers of the decoder network to shift and scale the features extracted from the input image. This process adds the details information captured in Z𝑍Z... | Deep generative models (DGMs) such as variational autoencoders (VAEs) [dayan1995helmholtz, vae, rezende2014stochastic] and generative adversarial networks (GANs) [gan] have enjoyed great success at modeling high dimensional data such as natural images. As the name suggests, DGMs leverage deep learning to model a data g... | B |
The structural computer used an inverted signal pair to implement the reversal of a signal (NOT operation) as a structural transformation, i.e. a twist, and four pins were used for AND and OR operations as a series and parallel connection were required. However, one can think about whether the four pin designs are the... |
Fig. 3 is AND and/or gate consisting of 3-pin based logics, Fig. 3 also shows the connection status of the output pin when A=0, B=1 is entered in the AND gate. when A=0, B=1, or A is connected, and B is connected, output C is connected only to the following two pins, and this is the correct result for AND operation. |
The structural computer used an inverted signal pair to implement the reversal of a signal (NOT operation) as a structural transformation, i.e. a twist, and four pins were used for AND and OR operations as a series and parallel connection were required. However, one can think about whether the four pin designs are the... | Optical logic aggregates can be designed in the same way as in Implementation of Structural Computer Using Mirrors and Translucent Mirrors, and for the convenience of expression and the exploration of mathematical properties (especially their association with matrices), the number shown in Fig. 5 can be applied to the ... |
The NOT gate can be operated in a logic-negative operation through one ‘twisting’ as in a 4-pin. To be exact, the position of the middle ground pin is fixed and is a structural transformation that changes the position of the remaining two true and false pins. | D |
Any permutation polynomial f(x)𝑓𝑥f(x)italic_f ( italic_x ) decomposes the finite field 𝔽qsubscript𝔽𝑞\mathbb{F}_{q}blackboard_F start_POSTSUBSCRIPT italic_q end_POSTSUBSCRIPT into sets containing mutually exclusive orbits, with the cardinality of each set being equal to the cycle length of the elements in that se... | Univariate polynomials f(x):𝔽→𝔽:𝑓𝑥→𝔽𝔽f(x):\mathbb{F}\to\mathbb{F}italic_f ( italic_x ) : blackboard_F → blackboard_F that induces a bijection over the field 𝔽𝔽\mathbb{F}blackboard_F are called permutation polynomials (in short, PP) and have been studied extensively in the literature. For instance, given a gene... | There has been extensive study about a family of polynomial maps defined through a parameter a∈𝔽𝑎𝔽a\in\mathbb{F}italic_a ∈ blackboard_F over finite fields. Some well-studied families of polynomials include the Dickson polynomials and reverse Dickson polynomials, to name a few. Conditions for such families of maps to... |
Given an n𝑛nitalic_n-dimensional vector space 𝔽nsuperscript𝔽𝑛\mathbb{F}^{n}blackboard_F start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT over finite field 𝔽𝔽\mathbb{F}blackboard_F, maps F:𝔽n→𝔽n:𝐹→superscript𝔽𝑛superscript𝔽𝑛F:\mathbb{F}^{n}\to\mathbb{F}^{n}italic_F : blackboard_F start_POSTSUPERSCRIPT ita... | The paper primarily addresses the problem of linear representation, invertibility, and construction of the compositional inverse for non-linear maps over finite fields. Though there is vast literature available for invertibility of polynomials and construction of inverses of permutation polynomials over 𝔽𝔽\mathbb{F}b... | B |
In this study we only considered different meta-learners within the MVS framework. Of course, many other algorithms for training classifiers exist. Some of those classifiers may be expected to perform better in terms of classification performance than the classifiers presented here, but not many have the embedded view... | In this article we investigated how different view-selecting meta-learners affect the performance of multi-view stacking. In our simulations, the interpolating predictor often performed worse than the other meta-learners on at least one outcome measure. For example, when the sample size was larger than the number of vi... |
For each experimental condition, we simulate 100 multi-view data training sets. For each such data set, we randomly select 10 views. In 5 of those views, we determine all of the features to have a relationship with the outcome. In the other 5 views, we randomly determine 50% of the features to have a relationship with... | Excluding the interpolating predictor, stability selection produced the sparsest models in our simulations. However, this led to a reduction in accuracy whenever the correlation within features from the same view was of a similar magnitude as the correlations between features from different views. In both gene expressi... | Any simulation study is limited by its choice of experimental factors. In particular, in our simulations we assumed that all features corresponding to signal have the same regression weight, and that all views contain an equal number of features. The correlation structures we used are likely simpler than those encounte... | D |
To study the impact of the anomaly percentage, we randomly select a certain percentage of objects and 10% of variables in each dataset to inject anomalous values. The percentage of anomalies range from 1% to 10%. The anomalies are generated by adding a perturbation to the original values and also ensure the perturbed v... |
Sensitivity Experiments: DepAD algorithms are not sensitive to the average correlation, sparseness, or dimensionality of datasets. DepAD methods exhibit stability when data contains noisy variables. However, the percentage of anomalies can negatively affect their effectiveness. |
Figure 11(b) demonstrates the impact of the number of noisy variables, ranging from 0 to 20, accounting for 0% to 18% of the original variables, with a fixed percentage of anomalies at 10%. FBED-CART-PS exhibits low sensitivity to noisy variables in terms of both ROC AUC and AP. This behavior can be attributed to the ... |
Regarding the experiments on noisy variables, we introduce noisy variables into the synthetic datasets following the process in existing literature [28]. Specifically, to ensure minimal dependency between the noisy and the original variables, the values of these noisy variables are drawn from a uniform distribution be... | The number of noisy variables: noisy variables are the variables that are unrelated to the data generation process. Research [86, 87, 28] has shown that these variables can hide the characteristics of anomalies, making anomaly detection more challenging.
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Δpred\del𝐗𝒬t,θsuperscriptΔpred\delsubscript𝐗subscript𝒬𝑡𝜃\Delta^{\text{pred}}\del{\mathbf{X}_{\mathcal{Q}_{t}},\theta}roman_Δ start_POSTSUPERSCRIPT pred end_POSTSUPERSCRIPT bold_X start_POSTSUBSCRIPT caligraphic_Q start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT end_POSTSUBSCRIPT , italic_θ represents the differen... | Algorithm 1 follows the template of in the face of uncertainty (OFU) strategies [Auer et al., 2002, Filippi et al., 2010, Faury et al., 2020]. Technical analysis of OFU algorithms relies on two key factors: the design of the confidence set and the ease of choosing an action using the confidence set.
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CB-MNL enforces optimism via an optimistic parameter search (e.g. in Abbasi-Yadkori et al. [2011]), which is in contrast to the use of an exploration bonus as seen in Faury et al. [2020], Filippi et al. [2010]. Optimistic parameter search provides a cleaner description of the learning strategy. In non-linear reward mo... | Comparison with Faury et al. [2020] Faury et al. [2020] use a bonus term for optimization in each round, and their algorithm performs non-trivial projections on the admissible log-odds. While we do reuse the Bernstein-style concentration inequality as proposed by them, their results do not seem to extend directly to th... | In this paper, we build on recent developments for generalized linear bandits (Faury et al. [2020]) to propose a new optimistic algorithm, CB-MNL for the problem of contextual multinomial logit bandits. CB-MNL follows the standard template of optimistic parameter search strategies (also known as optimism in the face of... | B |
We use an input sequence length L=1280𝐿1280L=1280italic_L = 1280, a channel dimension C=256𝐶256C=256italic_C = 256 throughout the network and a short factor γ=0.4𝛾0.4\gamma=0.4italic_γ = 0.4. We have 5 levels in the encoder and decoder pyramids respectively, with lengths L/2(l+1)𝐿superscript2𝑙1L/2^{(l+1)}italic_L ... | Datasets and evaluation metrics. We present our experimental results on two representative datasets THUMOS-14 (THUMOS for short) [15] and ActivityNet-v1.3 (ActivityNet for short) [7]. THUMOS-14 contains 413 temporally annotated untrimmed videos with 20 action categories, in which 200 videos are for training and 213 vid... |
The training batch size is 32 for both datasets. We train 10 epochs at learning rate 0.00005 for THUMOS and 15 epochs at learning rate 0.0001 for ActivityNet. We directly predict the 20 action categories for THUMOS; we conduct binary classification and then fuse our prediction scores with video-level classification sc... |
Implementation Details. In order to achieve higher performance, some works directly process video frames and learn features for the task of temporal action localization (TAL) in an end-to-end fashion [24, 42]. However, this has humongous requirements for GPU memory and computational capability. Instead, we follow the ... | Specifically, we propose a Video self-Stitching Graph Network (VSGN) for improving performance of short actions in the TAL problem. Our VSGN is a multi-level cross-scale framework that contains two major components: video self-stitching (VSS); cross-scale graph pyramid network (xGPN). In VSS, we focus on a short period... | B |
There are relevant works that involve the human in interpreting, debugging, refining, and comparing ensembles of models [DCCE19, LXL∗18, NP20, SJS∗18, XXM∗19, ZWLC19]. These papers use bagging [Bre01] and boosting [CG16, FSA99, KMF∗17] techniques for ranking and identifying the best combination of models in different ... | To provide a holistic view on the performance of the models for the selected validation metrics, we use a UMAP [MHM18] projection, as seen in Figure 2(a), that consists of the 500 randomly-sampled models (MDS [Kru64] and t-SNE [vdMH08] are also available).
Each model uses a set of particular hyperparameters, and it is ... | Moreover, the ranking of models is often based on a single validation metric, leading to the risks discussed in Section 1.
The aforementioned works that make use of genetic algorithms contain similar mechanisms as in VisEvol, but without VA support for (1) the exploration of the interconnected hyperparameters, and (2) ... | In the Sankey diagram (see Figure 3(a)), the user tracks the progress of the evolutionary process and is able to limit the number of models that will be generated through crossover and mutation for each algorithm (Step 4 in Figure 1). The default here is defined as user-selected random search value / 2222 for each algo... | VA tools have also been developed to visualize buckets of models [CAA∗19, TLKT09, ZWM∗19], where the best model for a specific problem is automatically chosen from a set of available options. These works feature exploration of the space in search for a final model, but the best model might not be the optimal when compa... | D |
The fundamental idea underlying MCMC algorithms is to synthesize a Markov chain that converges to a specified steady-state distribution.
Random sampling of a large state space while adhering to a predefined probability distribution is the predominant use of MCMC algorithms. | The current literature covers a broad spectrum of methodologies for Markov chain synthesis, incorporating both heuristic approaches and optimization-based techniques [4, 5, 6]. Each method provides specialized algorithms tailored to the synthesis of Markov chains in alignment with specific objectives or constraints.
Ma... | This algorithm treats the spatial distribution of swarm agents, called the density distribution, as a probability distribution and employs the Metropolis-Hastings (M-H) algorithm to synthesize a Markov chain that guides the density distribution toward a desired state.
The probabilistic guidance algorithm led to the dev... | Unlike the homogeneous Markov chain synthesis algorithms in [4, 7, 5, 6, 8, 9], the Markov matrix, synthesized by our algorithm, approaches the identity matrix as the probability distribution converges to the desired steady-state distribution. Hence the proposed algorithm attempts to minimize the number of state transi... | In this section, we apply the DSMC algorithm to the probabilistic swarm guidance problem and provide numerical simulations that show the convergence rate of the DSMC algorithm is considerably faster as compared to the previous Markov chain synthesis algorithms in [7] and [14].
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Other learning methods rely on a given template for each class [25] or local neighbourhood encoding to learn a compact representation [39].
The recently conducted SHREC correspondence contest on isometric and non-isometric 3D shapes [20] revealed that there is still room for improvement in both fields. | A shortcoming when applying the mentioned multi-shape matching approaches to isometric settings is that they do not exploit structural properties of isometric shapes. Hence, they lead to suboptimal multi-matchings, which we experimentally confirm in Sec. 5. One exception is the recent work on spectral map synchronisati... |
The multi-matching problem is relatively well-studied for generic settings, e.g. for matching multiple graphs [79, 78, 65, 6, 69, 77], or matching keypoints in image collections [76, 72, 42]. A desirable property of multi-matchings is cycle consistency (which we will formally define in Sec. 3.1). | Although multi-matchings obtained by synchronisation procedures are cycle-consistent, the matchings are often spatially non-smooth and noisy, as we illustrate in Sec. 5.
From a theoretical point of view, the most appropriate approach for addressing multi-shape matching is based on a unified formulation, where cycle con... | There are various works that particularly target the matching of multiple shapes. In [30, 32], semidefinite programming relaxations are proposed for the multi-shape matching problem. However, due to the employed lifting strategy, which drastically increases the number of variables, these methods are not scalable to lar... | B |
If there exists a polynomial algorithm that tests if a graph G𝐺Gitalic_G is a path graph and returns a clique path tree of G𝐺Gitalic_G when the answer is “yes”, then there exists an algorithm with the same complexity to test if a graph is a directed
path graph. |
In this section we introduce some results and notations in [1], that give a new characterization of path graphs resumed in Theorem 6. Indirectly, some of these results allow us to efficiently recognize directed path graphs too (see Section 5 and Theorem 9). | The paper is organized as follows. In Section 2 we present the characterization of path graphs and directed path graphs given by Monma and Wei [18], while in Section 3 we explain the characterization of path graphs by Apollonio and Balzotti [1]. In Section 4 we present our recognition algorithm for path graphs, we prov... | interval graphs ⊂ rooted path graphs ⊂ directed path graphs ⊂ path graphs ⊂ chordal graphs.interval graphs ⊂ rooted path graphs ⊂ directed path graphs ⊂ path graphs ⊂ chordal graphs\text{interval graphs $\subset$ rooted path graphs $\subset$ directed path %
graphs $\subset$ path graphs $\subset$ chordal graphs}.interva... | On the side of directed path graphs, at the state of art, our algorithm is the only one that does not use the results in [4], in which it is given a linear time algorithm able to establish whether a path graph is a directed path graph too (see Theorem 5 for further details). Thus, prior to this paper, it was necessary ... | A |
In this section, four real-world network datasets with known label information are analyzed to test the performances of our Mixed-SLIM methods for community detection. The four datasets can be downloaded from
http://www-personal.umich.edu/~mejn/netdata/. For the four datasets, the true labels are suggested by the origi... |
The ego-networks dataset contains more than 1000 ego-networks from Facebook, Twitter, and GooglePlus. In an ego-network, all the nodes are friends of one central user and the friendship groups or circles (depending on the platform) set by this user can be used as ground truth communities. The SNAP ego-networks are ope... | In this section, four real-world network datasets with known label information are analyzed to test the performances of our Mixed-SLIM methods for community detection. The four datasets can be downloaded from
http://www-personal.umich.edu/~mejn/netdata/. For the four datasets, the true labels are suggested by the origi... |
Dolphins: this network consists of frequent associations between 62 dolphins in a community living off Doubtful Sound. In the Dolphins network, node denotes a dolphin, and edge stands for companionship dolphins0 ; dolphins1 ; dolphins2 . The network splits naturally into two large groups females and males dolphins1 ; ... | The development of the Internet not only changes people’s lifestyles but also produces and records a large number of network structure data. Therefore, networks are often associated with our life, such as friendship networks and social networks, and they are also essential in science, such as biological networks (2002F... | C |
These works utilize the property that the diffusion process associated with Langevin dynamics in 𝒳𝒳\mathcal{X}caligraphic_X corresponds to the Wasserstein gradient flow of the KL-divergence in 𝒫2(𝒳)subscript𝒫2𝒳\mathcal{P}_{2}(\mathcal{X})caligraphic_P start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( caligraphic_X )
(Jo... | artifacts adopted only for theoretical analysis. We present the details of such a modified algorithm in Algorithm 2 in §A.
Without these modifications, Algorithm 2 reduces to the general method proposed in Algorithm 1, a deterministic particle-based algorithm, which is more advisable for | In addition to gradient-based MCMC, variational transport also shares similarity with Stein variational gradient descent (SVGD) (Liu and Wang, 2016), which is a more recent particle-based algorithm for Bayesian inference.
Variants of SVGD have been subsequently proposed. See, e.g., | In each iteration, variational transport approximates the update in (1.1) by first solving the dual maximization problem associated with the variational form of the objective and then using the obtained solution to specify a direction to push each particle.
The variational transport algorithm can be viewed as a forward... | Our Contribution. Our contribution is two fold. First, utilizing the optimal transport framework and the variational form of the objective functional, we propose a novel variational transport algorithmic framework for solving the distributional optimization problem via particle approximation.
In each iteration, variati... | B |
, i.e., each agent makes decision for its own. This type of methods is usually easy to scale, but may have difficulty to achieve global optimal performance due to the lack of collaboration. To address the problem, another way is to jointly model the action among learning agents with centralized optimization [16, 15]. H... | To make the policy transferable, traffic signal control is also modeled as a meta-learning problem in [14, 49, 36]. Specifically, the method in [14] performs meta-learning on multiple independent MDPs and ignores the influences of neighbor agents. A data augmentation method is proposed in [49] to generates diverse traf... | 2) The performances of Individual RL and PressLight drop 38% and 41% when the model is transferred. It shows that the models learned by the regular RL algorithms indeed rely on the training scenario. MetaLight is more robust to various scenarios than Individual RL and PressLight, and it indicates the advantage of the m... | We can obtain the following findings: 1) Among these 5 models, the performance of Baseline is the worst. The reason is that it is hard to learn the effective decentralized policy independently in the multi-agent traffic signal control task, where one agent’s reward and transition are affected by its neighbors. 2) Compa... |
In this paper, we propose a novel Meta RL method MetaVIM for multi-intersection traffic signal control, which can make the policy learned from a training scenario generalizable to new unseen scenarios. MetaVIM learns the decentralized policy for each intersection which considers neighbor information in a latent way. W... | A |
a curve {y=x2,z=x3}formulae-sequence𝑦superscript𝑥2𝑧superscript𝑥3\{y\,=\,x^{2},\,z\,=\,x^{3}\}{ italic_y = italic_x start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT , italic_z = italic_x start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT } along with three lines,
and a surface {x2+y2+z2= 1}superscript𝑥2superscript𝑦2superscrip... | Let 𝐱=(x1,x2,x3,x4)𝐱subscript𝑥1subscript𝑥2subscript𝑥3subscript𝑥4\mathbf{x}\,=\,(x_{1},x_{2},x_{3},x_{4})bold_x = ( italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 4 end_POSTSUBSCRI... | {x1=−x3,x2=−x4,x3x4=±1,t= 1}.formulae-sequencesubscript𝑥1subscript𝑥3formulae-sequencesubscript𝑥2subscript𝑥4formulae-sequencesubscript𝑥3subscript𝑥4plus-or-minus1𝑡1\{x_{1}\,=\,-x_{3},\,x_{2}\,=\,-x_{4},\,x_{3}\,x_{4}\,=\,\pm 1,~{}t\,=\,1\}.{ italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT = - italic_x start_POST... | the cyclic-4 system in 𝐱=(x1,x2,x3,x4)∈ℂ4𝐱subscript𝑥1subscript𝑥2subscript𝑥3subscript𝑥4superscriptℂ4\mathbf{x}\,=\,(x_{1},x_{2},x_{3},x_{4})\in\mathbbm{C}^{4}bold_x = ( italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 3 end_POSTSUBSC... | obtains a solution (x1,x2,x3,x4,t)subscript𝑥1subscript𝑥2subscript𝑥3subscript𝑥4𝑡(x_{1},x_{2},x_{3},x_{4},\,t)( italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT , italic_x start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT , i... | C |
While the standard online framework assumes that the algorithm has no information on the input sequence, a recently emerged and very active direction in Machine Learning seeks to leverage predictions on the input. More precisely, the algorithm has access to some machine-learned information on the input, which, however... |
We first present and analyze an algorithm called ProfilePacking, that achieves optimal consistency, and is also efficient if the prediction error is relatively small. The algorithm builds on the concept of a profile set, which serves as an approximation of the items that are expected to appear in the sequence, given t... |
Online bin packing was recently studied under an extension of the advice complexity model, in which the advice may be untrusted (?). Here, the algorithm’s performance is evaluated only at the extreme cases in which the advice is either error-free or adversarially generated, namely with respect to its consistency and i... | Our analysis of ProfilePacking, as stated in Theorem 3, in conjunction with the PAC-learnability of frequency predictions, can help obtain a sampling-based algorithm with an efficient tradeoff between the number of sampled items and its attained competitive ratio. More precisely, consider the setting in which the onlin... | Following the influential work (?), we refer to the competitive ratio of an algorithm with an error-free prediction as the consistency of the algorithm, and to the competitive ratio with an adversarial prediction as its robustness. Several online optimization problems have been studied in this learning-augmented settin... | D |
Finally, we empirically show the proposed framework produces high-fidelity and watertight meshes. It means that it solves the initial problem of disjoint patches occurring in the original AtlasNet (Groueix et al., 2018). To evaluate the continuity of output surfaces, we propose to use the following metric. |
In this experiment, we set N=105𝑁superscript105N=10^{5}italic_N = 10 start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT. Using more rays had a negligible effect on the output value of WT𝑊𝑇WTitalic_W italic_T but significantly slowed the computation. We compared AtlasNet with LoCondA applied to HyperCloud (HC) and HyperFl... |
The above formulation alone causes that many of the produced patches have unnecessarily long edges, and the network folds them, so the patch fits the surface of an object. To mitigate the issue, we add an edge length regularization motivated by (Wang et al., 2018). If we assume that the reconstructed mesh has the form... |
To leverage that knowledge, we express watertigthness as a ratio of rays that passed the parity test to the total number of all casted rays. Firstly, we sample N𝑁Nitalic_N points p∈S^𝑝^𝑆p\in\hat{S}italic_p ∈ over^ start_ARG italic_S end_ARG from all triangles of the reconstructed object S^^𝑆\hat{S}over^ start_ARG ... | Watertigthness Typically, a mesh is referred to as being either watertight or not watertight. Since it is a true or false statement, there is no well-established measure to define the degree of discontinuities in the object’s surface. To fill this gap, we propose a metric based on a simple, approximate check of whether... | D |
The Mirror-prox algorithm can be performed in a decentralized manner, however, it is not known whether its optimality is preserved.
In this paper, we prove that Mirror-prox remains optimal even in a decentralized case w.r.t. the dependence on the desired accuracy ε𝜀\varepsilonitalic_ε and condition number χ𝜒\chiitali... |
We demonstrate the performance of the DMP algorithm on different network architectures with different conditional number χ𝜒\chiitalic_χ: complete graph, star graph, cycle graph and the Erdős-Rényi random graphs with the probability of edge creation p=0.5𝑝0.5p=0.5italic_p = 0.5 and p=0.4𝑝0.4p=0.4italic_p = 0.4 under... | Paper organization. This paper is organized as follows. Section 2 presents a saddle point problem of interest along with its decentralized reformulation. In Section 3, we provide the main algorithm of the paper to solve such kind of problems. In Section 4, we present the lower complexity bounds for saddle point problem... | Finally, we show how the proposed method can be applied to prominent problem of computing Wasserstein barycenters to tackle the problem of instability of regularization-based approaches under a small value of regularizing parameter. The idea is based on the saddle point reformulation of the Wasserstein barycenter probl... |
We proposed a decentralized method for saddle point problems based on non-Euclidean Mirror-Prox algorithm. Our reformulation is built upon moving the consensus constraints into the problem by adding Lagrangian multipliers. As a result, we get a common saddle point problem that includes both primal and dual variables. ... | C |
Different classes of cycle bases can be considered. In [6] the authors characterize them in terms of their corresponding cycle matrices and present a Venn diagram that shows their inclusion relations. Among these classes we can find the strictly fundamental class. |
In the introduction of this article we mentioned that the MSTCI problem is a particular case of finding a cycle basis with sparsest cycle intersection matrix. Another possible analysis would be to consider this in the context of the cycle basis classes described in [6]. |
The length of a cycle is its number of edges. The minimum cycle basis (MCB) problem is the problem of finding a cycle basis such that the sum of the lengths (or edge weights) of its cycles is minimum. This problem was formulated by Stepanec [7] and Zykov [8] for general graphs and by Hubicka and Syslo [9] in the stric... |
The remainder of this section is dedicated to express the problem in the context of the theory of cycle bases, where it has a natural formulation, and to describe an application. Section 2 sets some notation and convenient definitions. In Section 3 the complete graph case is analyzed. Section 4 presents a variety of i... | where L^=D^tD^^𝐿superscript^𝐷𝑡^𝐷\hat{L}=\hat{D}^{t}\hat{D}over^ start_ARG italic_L end_ARG = over^ start_ARG italic_D end_ARG start_POSTSUPERSCRIPT italic_t end_POSTSUPERSCRIPT over^ start_ARG italic_D end_ARG is the lower right |V|−1×|V|−1𝑉1𝑉1|V|-1\times|V|-1| italic_V | - 1 × | italic_V | - 1 submatrix of the ... | B |
(m+1)𝑚1(m+1)( italic_m + 1 )-tuples of ℱℱ\mathcal{F}caligraphic_F with nonempty intersection. In other words, πm+1(ℱ)subscript𝜋𝑚1ℱ\pi_{m+1}(\mathcal{F})italic_π start_POSTSUBSCRIPT italic_m + 1 end_POSTSUBSCRIPT ( caligraphic_F ) is at least δ′=defρ/(mtm+1)superscriptdefsuperscript𝛿′𝜌binomial𝑚𝑡𝑚1\delta^{\prim... | a positive fraction of the m𝑚mitalic_m-tuples to have a nonempty intersection, where for dimK>1dimension𝐾1\dim K>1roman_dim italic_K > 1, m𝑚mitalic_m is some hypergraph Ramsey number depending on b𝑏bitalic_b and K𝐾Kitalic_K.
So in order to prove Corollary 1.3 it suffices to show that if a positive fraction of the ... | Lemma 4.6 assumes that the m𝑚mitalic_m-colored family ℱℱ\mathcal{F}caligraphic_F has the property that for 0≤j<dimK0𝑗dimension𝐾0\leq j<\dim K0 ≤ italic_j < roman_dim italic_K and for every colorful subfamily 𝒢𝒢\mathcal{G}caligraphic_G of ℱℱ\mathcal{F}caligraphic_F, the j𝑗jitalic_jth reduced Betti number β~j(⋂F∈�... | If we use Lemma 4.8 in place of Lemma 4.6 in the proof of Theorem 2.1, the hypothesis on the m𝑚mitalic_m-colored family ℱℱ\mathcal{F}caligraphic_F can be weakened. This “improved” Theorem 2.1 can in turn be applied in the proof of Theorem 1.2, yielding the following:
| The rest of Section 4.1 is devoted to the proof of Lemma 4.2. The proof first handles the case k=m𝑘𝑚k=mitalic_k = italic_m, and then uses it to prove the case k<m𝑘𝑚k<mitalic_k < italic_m. Note that for k>m𝑘𝑚k>mitalic_k > italic_m the lemma is trivial, as the chain group contains only a trivial chain and we can ta... | C |
Figure 1: Selecting important features, transforming them, and generating new features with FeatureEnVi: (a) the horizontal beeswarm plot for manually slicing the data space (which is sorted by predicted probabilities) and continuously checking the migration of data instances throughout the process; (b) the table heat... |
Automatic feature transformation has been examined within the ML community with positive results in reinforcement learning. In the work by Khurana et al. [1], the authors conduct a performance-driven exploration of a transformation graph which systematically enumerates the space of given options. A single “best” measu... | Workflow.
All experts commented that the workflow of FeatureEnVi is straightforward, because it is mainly linear despite involving optional iterative steps. E2 stated that feature engineering is usually very time consuming, especially without the support of a system like ours. E3 also agreed with us that the features h... | In machine learning (ML), classification is a type of supervised learning where the primary goal is to predict the dependent variable—also known as the target or class label—of every data instance (e.g., rows in a table) given independent features of the data (e.g., columns in a table). Feature engineering is the proce... | Figure 3: Exploration of features with FeatureEnVi. The default slicing thresholds for the data space separate the instances into four quadrants that represent intervals of 25% predicted probability (see (a.1–a.4)). View (b) presents a table heatmap with five different feature selection techniques and their average val... | C |
As expected, adding the global tracking error constraint increases the traversal time, but maintains the maximal deviation within the bounds (see the table in 5). This tracking error constraint results in a dramatic 5-fold decrease of the maximum deviation ‖e^c‖∞subscriptnormsubscript^𝑒𝑐\|\hat{e}_{c}\|_{\infty}∥ ove... | For the initialization phase needed to train the GPs in the Bayesian optimization, we select 20 samples over the whole range of MPC parameters, using Latin hypercube design of experiments. The BO progress is shown in Figure 5, right pannel, for the optimization with constraints on the jerk and on the tracking error. Af... | To reduce the number of times this experimental “oracle” is invoked, we employ Bayesian optimization (BO) [16, 17], which is an effective method for controller tuning [13, 18, 19] and optimization of industrial processes [20]. The constrained Bayesian optimization samples and learns both the objective function and the ... | which is an MPC-based contouring approach to generate optimized tracking references. We account for model mismatch by automated tuning of both the MPC-related parameters and the low level cascade controller gains, to achieve precise contour tracking with micrometer tracking accuracy. The MPC-planner is based on a combi... | MPC accounts for the real behavior of the machine and the axis drive dynamics can be excited to compensate for the contour error to a big extent, even without including friction effects in the model [4, 5]. High-precision trajectories or set points can be generated prior to the actual machining process following variou... | A |
Our study demonstrates that systems are highly sensitive to the tuning distribution, that explicit methods cannot handle multiple bias sources, and that more rigorous analysis is critical for bias mitigation algorithms for future progress. Based on our results, we argue that the community should focus on implicit meth... | Interestingly, MMD was low for digit position. We hypothesize this is because CNNs are unable to use position information for inference [42]. To confirm this, we add CoordConv layers [42] before and after the maxpooling layer in CNN to enable usage of position information. This resulted in methods exploiting digit posi... |
Methods are typically highly sensitive to hyperparameter choices, and papers report numbers on systems in which the hyperparameters were tuned using the test set distribution [18, 50, 64]. In the real world, biases may stem from multiple factors and may change in different environments, making this setup unrealistic. ... | Results.
In Fig. 3(a), we present the MMD boxplots for all bias variables, comparing cases when the label of the variable is either explicitly specified (explicit bias), or kept hidden (implicit bias) from the methods. Barring digit position, we observe that the MMD values are higher when the variables are not explicit... |
An interesting observation was that a weaker architecture, CNNs, were able to ignore position bias, whereas a more powerful architecture, CoordConv, resorted to exploiting this bias resulting in worse performance. While the community has largely focused on training procedures for bias mitigation, an exciting avenue fo... | D |
Some works seek to decompose the gaze into multiple related features and construct multi-task CNNs to estimate these feature. Yu et al. introduce a constrained landmark-gaze model for modeling the joint variation of eye landmark locations and gaze directions [119]. As shown in Fig. 9, they build a multi-task CNN to est... | Different types of input have been explored to extract features. Kellnhofer et al. directly extract features from facial images [43]. Zhou et al. combine the feature extracted from facial and eye images [84]. Palmero et al. use facial images, binocular images and facial landmarks to generate the feature vectors [79].
D... | Recasens et al. present an approach for following gaze in video by predicting where a person (in the video) is looking, even when the object is in a different frame [124].
They build a CNN to predict the gaze location in each frame and the probability containing the gazed object of each frame. Also, visual saliency sho... | Temporal information from videos also contributes to better gaze estimates. Recurrent Neural Network (RNN) has been widely used in video processing, e.g., long short-term memory (LSTM) [43, 84].
As shown in Fig. 5, they usually use a CNN to extract features from face images at each frame, and then input these features ... | Human gaze has a strong correlation with eye appearance. Even a minor perturbation in gaze direction can result in noticeable changes in eye appearance. For instance, when the eyeball rotates, the position of the iris and the shape of the eyelid undergo alterations, leading to corresponding changes in gaze direction. T... | B |
This deep quantization technique presents many advantages. It ensures a lightweight representation that makes the real-world masked face recognition process a feasible task. Moreover, the masked regions vary from one face to another, which leads to informative images of different sizes. The proposed deep quantization a... | The next step is to apply a cropping filter in order to extract only the non-masked region. To do so, we firstly normalize all face images into 240 ×\times× 240 pixels. Next, we partition a face into blocks. The principle of this technique is to divide the image into 100 fixed-size square blocks (24 ×\times× 24 pixels ... | Experimental results are carried out on Real-world Masked Face Recognition Dataset (RMFRD) and Simulated Masked Face Recognition Dataset (SMFRD) presented in wang2020masked . We start by localizing the mask region. To do so, we apply a cropping filter in order to obtain only the informative regions of the masked face (... | To tackle these problems, we distinguish two different tasks namely: face mask recognition and masked face recognition. The first one checks whether the person is wearing a mask or no. This can be applied in public places where the mask is compulsory. Masked face recognition, on the other hand, aims to recognize a face... |
The images of the used dataset are already cropped around the face, so we don’t need a face detection stage to localize the face from each image. However, we need to correct the rotation of the face so that we can remove the masked region efficiently. To do so, we detect 68 facial landmarks using Dlib-ml open-source l... | D |
\mathscr{A}]\triangleqitalic_F ∈ [ ⟨ ∗ , italic_x ⟩ ⇒ italic_P ( italic_x ) : italic_ϕ bold_⇒ script_A ] ≜ if ⋅;⋅⊢ϕ\cdot;\cdot\vdash\phi⋅ ; ⋅ ⊢ italic_ϕ, then F,proca(P(a))∈⟦a:𝒜⟧F,\operatorname{proc}a\,(P(a))\in\llbracket a:\mathscr{A}\rrbracketitalic_F , roman_proc italic_a ( italic_P ( italic_a ) ) ∈ ⟦ italic_a : sc... |
The first rule for →→\to→ corresponds to the identity rule and copies the contents of one cell into another. The second rule, which is for cut, models computing with futures [Hal85]: it allocates a new cell to be populated by the newly spawned P𝑃Pitalic_P. Concurrently, Q𝑄Qitalic_Q may read from said new cell, which... | Positive semantic types are defined by intension—the contents of a particular cell—whereas negative semantic types are defined by extension—how interacting with a continuation produces the desired result. Analogously for the λ𝜆\lambdaitalic_λ-calculus, the semantic positive product is defined as containing pairs of te... |
For space, we omit the process terms. Of importance is the instance of the call rule for the recursive call to eat: the check i−1<i𝑖1𝑖i-1<iitalic_i - 1 < italic_i verifies that the process terminates and the loop [(i−1)/i][z/x]Ddelimited-[]𝑖1𝑖delimited-[]𝑧𝑥𝐷[(i-1)/i][z/x]D[ ( italic_i - 1 ) / italic_i ] [ ita... | With these compatibility lemmas in hand, we are almost ready to construct a correspondence between the syntactic typing of processes and configuration objects with the semantic typing thereof. First, we need a semantic interpretation of (syntactic) types.
| B |
First, the owner requires that the cloud not be able to obtain the plaintext about the media content and the LUTs, and that access to the media content is controlled by his/her authorization.
Second, the owner asks for significant overhead savings from cloud media sharing. Third, the owner demands traitor tracing of us... |
The threats considered in this paper come from three entities: users, the owner, and the cloud. First, users are assumed to be malicious, who could illegally redistribute the owner’s media content with the hope that this behavior will not be detected. Second, the owner is also assumed to be malicious, who may try to o... | Implement privacy-preserving access control. On the one hand, the cloud should be prevented from obtaining the private plaintext of the data it encounters, including the owner’s media content, the users’ fingerprints, and the LUTs. On the other hand, only users authorized by the owner can access the media content.
| Users. Users want to access the owner’s media content. To this end, users request authorization from the owner, for example by paying for purchases. If successful, users can get the desired shared media content from the cloud. Users require that the plaintext of their fingerprints not be accessed by the owner or the cl... | First, the owner requires that the cloud not be able to obtain the plaintext about the media content and the LUTs, and that access to the media content is controlled by his/her authorization.
Second, the owner asks for significant overhead savings from cloud media sharing. Third, the owner demands traitor tracing of us... | C |
This section presents an empirical investigation of the performance of GraphFM on two CTR benchmark datasets and a recommender system dataset. The experimental settings are described, followed by comparisons with other state-of-the-art methods. An ablation study is also conducted to verify the importance of each compo... | Our proposed GraphFM achieves best performance among all these four classes of methods on three datasets. The performance improvement of GraphFM compared with the three classes of methods (A, B, C) is especially significant, above 0.010.01\mathbf{0.01}bold_0.01-level. The aggregation-based methods including InterHAt, A... | Since our proposed approach selects the beneficial feature interactions and models them in an explicit manner, it has high efficiency in analyzing high-order feature interactions and thus provides rationales for the model outcome.
Through extensive experiments conducted on CTR benchmark and recommender system datasets,... | Our experiments are conducted on three real-world datasets, two CTR benchmark datasets, and one recommender system dataset. Details of these datasets are illustrated in Table 1.
The data preparation follows the strategy in Tian et al. (2023). We randomly split all the instances in 8:1:1 for training, validation, and te... | (2) By treating features as nodes and their pairwise feature interactions as edges, we bridge the gap between GNN and FM, and make it feasible to leverage the strength of GNN to solve the problem of FM.
(3) Extensive experiments are conducted on CTR benchmark and recommender system datasets to evaluate the effectivenes... | C |
\mathcal{L}_{0}}\delta^{2}}{4\tilde{L}D^{2}}\right)^{\left\lceil(t-1)/2\right%
\rceil}.italic_h ( bold_x start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT ) ≤ italic_h ( bold_x start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT ) ( 1 - divide start_ARG italic_μ start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT start_POSTSUPERSCRIPT cal... | We also show improved convergence rates for several variants in various cases of interest and prove that the AFW [Wolfe, 1970, Lacoste-Julien & Jaggi, 2015] and BPCG Tsuji et al. [2022] algorithms coupled with the backtracking line search of Pedregosa et al. [2020] can achieve linear convergence rates over polytopes wh... |
Furthermore, with this simple step size we can also prove a convergence rate for the Frank-Wolfe gap, as shown in Theorem 2.6. More specifically, the minimum of the Frank-Wolfe gap over the run of the algorithm converges at a rate of 𝒪(1/t)𝒪1𝑡\mathcal{O}(1/t)caligraphic_O ( 1 / italic_t ). The idea of the proof is... | We can make use of the proof of convergence in primal gap to prove linear convergence in Frank-Wolfe gap. In order to do so, we recall a quantity formally defined in Kerdreux et al. [2019] but already implicitly used earlier in Lacoste-Julien & Jaggi [2015] as:
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When the domain 𝒳𝒳\mathcal{X}caligraphic_X is a polytope, one can obtain linear convergence in primal gap for a generalized self-concordant function using the well known Away-step Frank-Wolfe (AFW) algorithm [Guélat & Marcotte, 1986, Lacoste-Julien & Jaggi, 2015] shown in Algorithm 5 | C |
In particular, it is desirable that the number of passes is independent of the input graph size.
We call an algorithm a k𝑘kitalic_k-pass algorithm if the algorithm makes k𝑘kitalic_k passes over the edge stream, possibly each time in a different order [MP80, FKM+05]. | This model is not only interesting for massive data sets but also whenever there is no random access to the input, for instance, if the input is only defined implicitly.
Moreover, many insights and techniques from this model naturally carry over to a variety of areas in theoretical computer science, including communica... | The problem of finding an arbitrarily good approximation has been studied in the streaming model [Ber88, ALT21, KN21] on bipartite graphs as well as various related models that deal with non-random access to the input.
For instance, there are works in the setting of dynamic streams where edges can be added and removed ... | Maximum Matching is one of the most fundamental problems in combinatorial optimization and has been extensively studied in the classic centralized model of computation for almost half a century. We refer to [Sch03] for an overview. In particular, several exact polynomial-time deterministic maximum matching algorithms a... | For massive graphs the classical matching algorithms are not only prohibitively slow, but also space complexity becomes a concern. If a graph is too large to fit into the memory of a single machine, all the classical algorithms—which assume random access to the input—are not applicable.
This demand for a more realistic... | A |
When b=6𝑏6b=6italic_b = 6 or k=20𝑘20k=20italic_k = 20, the trajectories of CPP are very close to that of exact Push-Pull/𝒜ℬ𝒜ℬ\mathcal{A}\mathcal{B}caligraphic_A caligraphic_B, which indicates that when the compression errors are small, they are no longer the bottleneck of convergence.
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Figure 3: Performance of Push-Pull/𝒜ℬ𝒜ℬ\mathcal{A}\mathcal{B}caligraphic_A caligraphic_B, CPP, B-CPP against the number of transmitted bits: the left column shows the results with quantization (b=2,4,6𝑏246b=2,4,6italic_b = 2 , 4 , 6) and the right column shows the results with Rand-k (k=5,10,20𝑘51020k=5,10,20ital... |
To see why CPP outperforms Push-Pull/𝒜ℬ𝒜ℬ\mathcal{A}\mathcal{B}caligraphic_A caligraphic_B, note that the vectors sent in CPP have been compressed, and hence the transmitted bits at each iteration are greatly reduced compared to Push-Pull/𝒜ℬ𝒜ℬ\mathcal{A}\mathcal{B}caligraphic_A caligraphic_B. |
Figure 1: Linear convergence of Push-Pull/𝒜ℬ𝒜ℬ\mathcal{A}\mathcal{B}caligraphic_A caligraphic_B, CPP, and B-CPP with b𝑏bitalic_b bit quantization (b=2,4,6𝑏246b=2,4,6italic_b = 2 , 4 , 6) and Rand-k (k=5,10,20𝑘51020k=5,10,20italic_k = 5 , 10 , 20) compressors. | We can see from all of the sub-figures of Fig. 3 that, to reach a high accuracy within about 10−15superscript101510^{-15}10 start_POSTSUPERSCRIPT - 15 end_POSTSUPERSCRIPT, the number of transmitted bits required by these methods have the ranking: B-CPP <<< CPP <<< Push-Pull/𝒜ℬ𝒜ℬ\mathcal{A}\mathcal{B}caligraphic_A ca... | D |
where x1,…,xMsubscript𝑥1…subscript𝑥𝑀x_{1},\ldots,x_{M}italic_x start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , italic_x start_POSTSUBSCRIPT italic_M end_POSTSUBSCRIPT and y1,…,yMsubscript𝑦1…subscript𝑦𝑀y_{1},\ldots,y_{M}italic_y start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , italic_y start_POSTSUBSCRIPT italic_M end... | Unlike (2), the formulation (1) penalizes not the difference with the global average, but the sameness with other connected local nodes. Thereby the decentralized case can be artificially created in centralized architecture, e.g., if we want to create the network and W𝑊Witalic_W matrix to connect only some clients bas... | Note that in the proposed formulation (1) we consider both the centralized and decentralized cases. In the decentralized setting, all nodes are connected within a network, and each node can communicate/exchange information only with their neighbors in the network. While the centralized architecture consists of master-s... |
In this paper, we present a novel formulation for the Personalized Federated Learning Saddle Point Problem (1). This formulation incorporates a penalty term that accounts for the specific structure of the network and is applicable to both centralized and decentralized network settings. Additionally, we provide the low... | To the best of our knowledge, this paper is the first to consider decentralized personalized federated saddle point problems, propose optimal algorithms and derives the computational and communication lower bounds for this setting. In the literature, there are works on general (non-personalized) SPPs. We make a detaile... | B |
A (C)CE MS provides a distribution that is in equilibrium over the set of joint policies found so far, Π0:tsuperscriptΠ:0𝑡\Pi^{0:t}roman_Π start_POSTSUPERSCRIPT 0 : italic_t end_POSTSUPERSCRIPT. For the algorithm to have converged, it needs to also be in equilibrium over the set of all possible joint policies, Π∗supe... |
PSRO consists of a response oracle that estimates the best response (BR) to a joint distribution of policies. Commonly the response oracle is either a reinforcement learning (RL) agent or a method that computes the exact BR. The component that determines the distribution of policies that the oracle responds to is call... | We evaluate a number of (C)CE MSs in JPSRO on pure competition, pure cooperation, and general-sum games (Section H). All games used are available in OpenSpiel (Lanctot et al., 2019). More thorough descriptions of the games used can be found in Section F. We use an exact BR oracle, and exactly evaluate policies in the m... | We have shown that JPSRO converges to an NF(C)CE over joint policies in extensive form and stochastic games. Furthermore, there is empirical evidence that some MSs also result in high value equilibria over a variety of games. We argue that (C)CEs are an important concept in evaluating policies in n-player, general-sum ... |
In Section 2 we provide background on a) correlated equilibrium (CE), an important generalization of NE, b) coarse correlated equilibrium (CCE) (Moulin & Vial, 1978), a similar solution concept, and c) PSRO, a powerful multi-agent training algorithm. In Section 3 we propose novel solution concepts called Maximum Gini ... | B |
Another line of work (e.g., Gehrke et al. (2012); Bassily et al. (2013); Bhaskar et al. (2011)) proposes relaxed privacy definitions that leverage the natural noise introduced by dataset sampling to achieve more average-case notions of privacy. This builds on intuition that average-case privacy can be viewed from a Bay... | One cluster of works that steps away from this worst-case perspective focuses on giving privacy guarantees that are tailored to the dataset at hand (Nissim et al., 2007; Ghosh and Roth, 2011; Ebadi et al., 2015; Wang, 2019). In Feldman and Zrnic (2021) in particular, the authors elegantly manage to track the individua... |
Differential privacy essentially provides the optimal asymptotic generalization guarantees given adaptive queries (Hardt and Ullman, 2014; Steinke and Ullman, 2015). However, its optimality is for worst-case adaptive queries, and the guarantees that it offers only beat the naive intervention—of splitting a dataset so ... |
An alternative route for avoiding the dependence on worst case queries and datasets was achieved using expectation based stability notions such as mutual information and KL stability Russo and Zou (2016); Bassily et al. (2021); Steinke and Zakynthinou (2020). Using these methods Feldman and Steinke (2018) presented a ... | Another line of work (e.g., Gehrke et al. (2012); Bassily et al. (2013); Bhaskar et al. (2011)) proposes relaxed privacy definitions that leverage the natural noise introduced by dataset sampling to achieve more average-case notions of privacy. This builds on intuition that average-case privacy can be viewed from a Bay... | C |
We have taken the first steps into a new direction for preprocessing which aims to investigate how and when a preprocessing phase can guarantee to identify parts of an optimal solution to an 𝖭𝖯𝖭𝖯\mathsf{NP}sansserif_NP-hard problem, thereby reducing the running time of the follow-up algorithm. Aside from the techni... |
As the first step of our proposed research program into parameter reduction (and thereby, search space reduction) by a preprocessing phase, we present a graph decomposition for Feedback Vertex Set which can identify vertices S𝑆Sitalic_S that belong to an optimal solution; and which therefore facilitate a reduction fr... | We have taken the first steps into a new direction for preprocessing which aims to investigate how and when a preprocessing phase can guarantee to identify parts of an optimal solution to an 𝖭𝖯𝖭𝖯\mathsf{NP}sansserif_NP-hard problem, thereby reducing the running time of the follow-up algorithm. Aside from the techni... |
This line of investigation opens up a host of opportunities for future research. For combinatorial problems such as Vertex Cover, Odd Cycle Transversal, and Directed Feedback Vertex Set, which kinds of substructures in inputs allow parts of an optimal solution to be identified by an efficient preprocessing phase? Is i... | The goal of this paper is to open up a new research direction aimed at understanding the power of preprocessing in speeding up algorithms that solve NP-hard problems exactly [26, 31]. In a nutshell, this new direction can be summarized as: how can an algorithm identify part of an optimal solution in an efficient prepro... | C |
Painterly image harmonization: In standard image harmonization, both foreground and background are from realistic images. There exist certain application scenarios that the background is an artistic image while the foreground is from a realistic image, in which case the standard image harmonization models may not work ... | For example, Luan et al. [104] proposed to optimize the input image with two passes, in which the first pass aims at robust coarse harmonization and the second pass targets at high-quality refinement.
Feed-forward methods send the input image through the model to output the harmonized result. For example, Peng et al. [... |
Image harmonization is closely related to style transfer. Note that both artistic style transfer [37, 56, 118] and photorealistic style transfer [103, 82] belong to style transfer. Image harmonization is closer to photorealistic style transfer, which transfers the style of a reference photo to another input photo. The... | Painterly image harmonization is more challenging because multiple levels of styles (i.e., color, simple texture, complex texture) [115] need to be transferred from background to foreground, while standard image harmonization only needs to transfer low-level style (i.e., illumination).
Painterly image harmonization is ... | Painterly image harmonization: In standard image harmonization, both foreground and background are from realistic images. There exist certain application scenarios that the background is an artistic image while the foreground is from a realistic image, in which case the standard image harmonization models may not work ... | C |
Transfer learning: Firstly, it can serve as an ideal testbed for transfer learning algorithms, including meta-learning [5], AutoML [23], and transfer learning on spatio-temporal graphs under homogeneous or heterogeneous representations. In the field of urban computing, it is highly probable that the knowledge required ... | In the present study, we have introduced CityNet, a multi-modal dataset specifically designed for urban computing in smart cities, which incorporates spatio-temporally aligned urban data from multiple cities and diverse tasks. To the best of our knowledge, CityNet is the first dataset of its kind, which provides a comp... |
As depicted in Table V, deep learning models can generate highly accurate predictions when provided with ample data. However, the level of digitization varies significantly among cities, and it is likely that many cities may not be able to construct accurate deep learning prediction models due to a lack of data. One e... | To the best of our knowledge, CityNet is the first multi-modal urban dataset that aggregates and aligns sub-datasets from various tasks and cities. Using CityNet, we have provided a wide range of benchmarking results to inspire further research in areas such as spatio-temporal predictions, transfer learning, reinforcem... | Federated learning: Secondly, CityNet is an appropriate dataset to investigate various federated learning topics under different settings, with each party holding data from one source or one city. Urban data is usually generated by a multitude of human activities and stored by diverse stakeholders, such as organization... | D |
𝒞(Γ,P):=E(𝐱,y)∼P[𝟙(y∈Γ(𝐱))]=Prob{y∈Γ(𝐱)},assign𝒞Γ𝑃subscriptEsimilar-to𝐱𝑦𝑃delimited-[]1𝑦Γ𝐱Prob𝑦Γ𝐱\displaystyle\mathcal{C}(\Gamma,P):=\mathrm{E}_{(\mathbf{x},y)\sim P}\big{[}%
\mathbbm{1}(y\in\Gamma(\mathbf{x}))\big{]}=\text{Prob}\{y\in\Gamma(\mathbf{x})% |
where 𝟙1\mathbbm{1}blackboard_1 denotes the indicator function and P𝑃Pitalic_P denotes the joint distribution on 𝒵𝒵\mathcal{Z}caligraphic_Z, a significance or confidence level α𝛼\alphaitalic_α is chosen faulkenberry1973method ; fraser1956tolerance such that |
where 𝟙y≤y∗subscript1𝑦superscript𝑦\mathbbm{1}_{y\leq y^{*}}blackboard_1 start_POSTSUBSCRIPT italic_y ≤ italic_y start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT end_POSTSUBSCRIPT denotes the indicator function of the set {y∈ℝ:y≤y∗}conditional-set𝑦ℝ𝑦superscript𝑦\{y\in\mathbb{R}:y\leq y^{*}\}{ italic_y ∈ blackboard_R :... | By differentiating the argument on the right-hand side with respect to q𝑞qitalic_q and equating it to 0, one obtains definition (19) of the α𝛼\alphaitalic_α-quantile. The pinball loss (26) is then simply the loss function for the sample α𝛼\alphaitalic_α-quantile, i.e. the α𝛼\alphaitalic_α-quantile of the empirical ... | In this section the models that predict the lower and upper bounds of prediction intervals are considered, for example the α/2𝛼2\alpha/2italic_α / 2- and (1−α/2)1𝛼2(1-\alpha/2)( 1 - italic_α / 2 )-quantile estimates for a given significance level α𝛼\alphaitalic_α. For this class of estimators a reasonable choice of ... | A |
Despite the fame of BERT, we are aware of only two publications that employ BERT-like PTMs for symbolic music classification \parencitetsai20ismir,musicbert.
The first work \parencitetsai20ismir deals with optically scanned sheet music, while we use MIDI inputs. | Throughout this article, we refer to note-level classification tasks as tasks that perform a prediction for each individual note in a music sequence and sequence-level tasks as tasks that require a single prediction for an entire music sequence. We consider two note-level tasks and two sequence-level tasks in our exper... | Machine learning has been applied to music in symbolic formats such as MIDI. Exemplary tasks include symbolic-domain music genre classification \parencitecorrea16survey,ferraro18, composer classification \parencitelee20ismirLBD,kong2020largescale,
and melody note identification \parencitesimonettaCNW19, note-affinity. |
Table 2: The testing classification accuracy (in %) of different combinations of MIDI token representations and models for four downstream tasks: three-class melody classification, velocity prediction, style classification and emotion classification. “CNN” represents the ResNet50 model used by \textcitelee20ismirLBD, ... | We evaluate PTMs on four piano music classification tasks.
These include two note-level classification tasks, i.e., melody extraction \parencitesimonettaCNW19,note-affinity and velocity prediction \parencitewidmer94aaai,jeongKKLN19ismir,jeongKKN19icml and two sequence-level classification tasks, i.e., style classificat... | D |
Otherwise, F𝐹Fitalic_F has a leaf v∈A𝑣𝐴v\in Aitalic_v ∈ italic_A with a neighbor u∈B𝑢𝐵u\in Bitalic_u ∈ italic_B. We can assign c(v)=a2𝑐𝑣subscript𝑎2c(v)=a_{2}italic_c ( italic_v ) = italic_a start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT, c(u)=b2𝑐𝑢subscript𝑏2c(u)=b_{2}italic_c ( italic_u ) = italic_b start_POSTSU... | To obtain the total running time we first note that each of the initial steps – obtaining (R,B,Y)𝑅𝐵𝑌(R,B,Y)( italic_R , italic_B , italic_Y ) from Corollary 2.11 (e.g. using Algorithm 1), contraction of F𝐹Fitalic_F into F′superscript𝐹normal-′F^{\prime}italic_F start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT, and findi... | The linear running time follows directly from the fact that we compute c𝑐citalic_c only once and we can pass additionally through recursion the lists of leaves and isolated vertices in an uncolored induced subtree. The total number of updates of these lists is proportional to the total number of edges in the tree, hen... | Next, let us count the total number of jumps necessary for finding central vertices over all loops in Algorithm 1. As it was stated in the proof of Lemma 2.2, while searching for a central vertex we always jump from a vertex to its neighbor in a way that decreases the largest remaining component by one. Thus, if in the... |
Now, observe that if the block to the left is also of type A, then a respective block from Z(S)𝑍𝑆Z(S)italic_Z ( italic_S ) is (0,1,0)010(0,1,0)( 0 , 1 , 0 ) – and when we add the backward carry (0,0,1)001(0,0,1)( 0 , 0 , 1 ) to it, we obtain the forward carry to the rightmost block. And regardless of the value of t... | B |
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